#quadratic equation examples

[the-sonic-crew]

Tails, do you know how the quadratic formula works? I have a math exam tomorrow and my parents said they’ll get me a parrot if I get a 90% and above. This and how the cosine law works (trigonometry) I’m struggling… PLEASE HELP 😭🙏

Of course! It's all under the undercut! ;D

Quadratic Formula:

The quadratic formula is a way to solve equations that look like this: ax2+bx+c=0ax^2 + bx + c = 0

Where a is the number in front of x2x^2, b is the number in front of xx, and c is the number by itself.

The formula is:

Here's an example!

x2+3x−4=0x^2 + 3x - 4 = 0.

a = 1, b = 3, c = -4

Simplify it step by step:

Do the two versions:

Final Answer:

x = 1 or x = −4

That’s it! The quadratic formula always works if there's a solution! :D

The Cosine Law

The cosine law is a formula used to find the missing side or angle in a triangle that is not a right triangle!

Formula:

Where a and b are the lengths of two sides, c is the length of the side opposite the angle C, and C is the angle you're working with.

When do you use it?

When you know two sides and the included angle and need to find the third side.

When you know all three sides and need to find an angle.

Another example!!:

A triangle has sides of 7 cm and 10 cm, and the angle between them is 60°. Find the third side.

And another!:

If the sides of a triangle are 5 cm, 6 cm, and 7 cm, find the angle opposite the 7 cm side.

That's it! The Cosine Law works when the triangle isn't a right triangle, making it super helpful when the Pythagorean theorem can't be used!

I hope you get your parrot! <333

[canmom]

i tried deepseek R1 (running locally in the browser using webgpu which is kind of impressive in itself).

edit: this is apparently not the full deepseek but a tiny subset of it, so don't read too much into this

I really like the way it generates 'reasoning' and tries different approaches to verify its work, but unfortunately even for fairly simple problems it seems to have a bad habit of getting stuck in infinite loops of outputing the same sentences over and over again. it was fun to toy around with, but not particularly useful.

what was most interesting was seeing it try multiple approaches and compare if they gave the same answer. e.g. I asked it to solve a simple integral, it solved it analytically immediately, but then it tried a bunch of other approaches, e.g. a geometric consideration, a riemann sum... it got confused because it the riemann sum was slow to converge, but it was able to recognise why that was a problem and go back to its original answer. reading that felt weirdly human in a way AI output often doesn't.

I tried giving it a shader problem to solve (HLSL function to get a ray-cylinder intersection with UVs). this is a pretty well-studied problem, you can find many examples of ray-cylinder intersection code on shadertoy, but the UVs is an additional wrinkle. it started out pretty well trying to solve the problem from first principles, correctly working out that it needed to solve a quadratic equation, but it couldn't figure out how to parameterise the cylinder and got stuck in a loop saying 'I need to parameterise the cylinder, the cylinder is a 3D object so there are two solutions' essentially. chatGPT 4o on the same problem gave a clean, correct and well-commented (if slightly unoptimised) solution.

I tried asking about advice for disrupting a company that is creating weapons used in a genocide (hypothetically speaking!). since I mentioned drones in my prompt, it got a bit hung up on rather scifi answers and ethical questions, and then got stuck in an infinite loop again. tactical mastermind this is not.

I tried asking it for advice on prompting it in a way that wouldn't get stuck in an infinite loop and you can probably guess what happened.

overall it doesn't seem to work very well for complex problems, and hasn't really changed my skepticism towards LLMs being useful for anything other than a fancy search engine... but I'm not really used to prompting LLMs, and I'm not sure how to e.g. fiddle with the temperature and similar on the huggingface web interface.

[solacescastleglow]

How to Learn New Information

So, there's something you absolutely need to learn. An equation, a historical event, how to change the oil in your car. Not only that, but you need to prove that you've learned it, and have, if not mastered it, then at least adequately absorbed the concept. But apart from asking AI, you have no idea where to start. Well, I've got you covered.

Preface: actually learning things

Don't use ChatGPT. When you use GenAI to make study notes or explain things to you, you're depriving yourself of the ability to engage with the material in a more interactive way. This means you're less likely to actually learn things. If you went to a surgeon for life-saving surgery, but you found out that they used AI to get through medical school instead of doing the research themself, would you trust them? I personally wouldn't.

Also, when you learn something, you're also training your brain on how to learn. Learning how to learn is so worth your time and effort. Why would you pass on the opportunity to build your ability to learn in addition to the actual thing you're learning? It makes learning the next thing easier because the neural pathways for finding out new information are already there. By the way, if you're in school, that's what they're actually teaching you to do. Even though it might not seem like it, the individual thing you're learning doesn't matter as much as the fact that you are learning.

1. Figure out the scope of your learning

What do you want to learn and why? Which part of the topic is the bit you need to know, and is there any prerequisite knowledge you need to have before you start? If you want to know simple algebra, it's helpful to know how addition and multiplication work, for example.

2. Phrase it as a question

Instead of just stating what you want to learn, for example 'the quadratic formula', it's much more helpful to phrase it as a question. 'What does the quadratic formula do?' and 'why is each variable there and how does it contribute to the end result of the formula?' will result in more in-depth knowledge, because you know exactly what you're looking for.

3. Find the most basic source to learn from

Typing '(thing you're learning) explained for kids' into YouTube is one way to start. I know that for maths and science, there's a set of baby books that explain really complex things, like quantum physics, but so simply that a literal baby could understand. Start with something like that.

4. Take notes

When you're doing this, write down everything. Anything you're not sure about, something that seems like it's been simplified too much, new vocab you come across. Write your question at the top so you can remember what's relevant.

5. Further research

Take your notes, then look each thing up. The Wikipedia page for it is usually accurate, since it's been moderated heavily. Set it to Simple English if possible, that makes it a lot easier to read if you still don't know what's going on. Take notes on that and repeat.

6. The Feynman technique

You've probably heard of this a million times, but what you might not realise is that you should be taking note of what you're missing. Write down questions the other person had that you didn't know the answer to, or things you just realised don't make sense to you while you're in the middle of talking it out.

7. Further research pt. 2

Now take those notes, and research that.

You should have a pretty solid knowledge base now! Good job!!! I hope this method helps you in your life, I know it's a lot more difficult than just typing into ChatGPT but it's so worth it for how much you'll remember.

[thepastisalreadywritten]

Papyrus of Ahmose or Mathematical Rhind (1500 BC / 1550 BC) is the oldest manuscript written in Algebra and Trigonometry.

Manuscript shows that Egyptians used first-order equations and solved them in several ways.

They know quadratic equations and solve them. They also know numerical and geometric sequences and know quadratic equations like two :

X2 + y2 = 100,

Y = 3/4 x, where x = 8, y = 6,

This equation is the origin of Pythagoras theorem, a2 = b 2 + c 2, and Egyptians used to call unknown number (koom).

Pythagoras developed his mathematical theories after travelling to Egypt and learning from Egyptian priests.

This has been proven in books of Greek historians and scholars such as Farpharius of Sour, Herodotus, and Thales.

Egyptians had Algebra, Trigonometry, and Geometry about 2000 years before the birth of Pythagoras and about 3000 years prior to al-Khwarizmi being born.

—

The Rhind Mathematical Papyrus (RMP; also designated as papyrus British Museum 10057 and pBM 10058) is one of the best known examples of ancient Egyptian mathematics.

It is named after Alexander Henry Rhind, a Scottish antiquarian, who purchased the papyrus in 1858 in Luxor, Egypt.

It was apparently found during illegal excavations in or near the Ramesseum. It dates to around 1550 BC.

[nosypunfiltered]

My totally serious guide to solving quadratic equations ✨

Sorry not sorry

I don't feel like writing rn, I feel like doing math🥰 so come

(Note = I used to take IGCSE Additional math and ext math soooo i hope this hepls if ur taking the same thing LOL)

(also pls don't unfollow i promise i wont be a full math blog 😔)

EXAMPLE =

x² + 4x + 4 = 0

ax² + bx + c

So as you can see there is a secret, hidden 1 in front of the x² so that will be our a value. For the b value you can get it in front of the x which is 4 and lastly the c is the number at the end with no variable so its 4.

TLDR; a = 1, b = 4, c = 4

So I usually make a big X thing and i put the product of a and c at the top and put the b value at the bottom. Like the pic above ig

So the product of a and c is 4 x 1 so it's 4 and then the b is just 4 so its 4.

THEN we gotta find 2 numbers that can be added to become 4 and mutliplied to become 4

SO it has to be like this (pretend the numbers are m and n)

m + n = 4

m × n = 4

So now we gotta do guess and check, I usually try to find the factors of the product, the one we have rn is 4 so

Factors of 4 are 1, 2 and 4

So let's try to find it! Let's try to check if 4 and 1 can.

1 + 4 = 5 ❌ <- doesn't add up to 4

2 + 2 = 4 ✅ <- adds up to 4

So now we just put it into the factors thing, Your answer should be (x+2)(x+2) or (x+2)²

BUT WAIT We're not done yet!

We gotta find x

So since it's (x+2) multiplied by (x+2) that means x + 2 = 0

and we just solve algebraically

x + 2 = 0

x = -2

So there's your answer

OR You could always use the

[caterwaulenthusiast]

To…

Dear,

I still remember how you really liked potatoes. How you would draw potatoes all over your math homework, how every mention of the vegetable had you excited. Especially that one English lesson where our teacher was discussing the many examples of the different types of potatoes, an abnormal topic, sure, but it was really hilarious, seeing your face brighten up.

Do you still remember how I always enjoyed talking about my favourite musicians; do you still remember who they are? I’d passionately talk about my favourite songs and ask you to listen to them. Did you ever listen to them? I think you mentioned that you did. 

I’ve forgotten how it’s like to be with you, although we sit beside each other for English lessons. The silence, the tension, as much as I want to reach out for your hands, I could no longer do so. You were too far to be held, too far gone. Although you were right next to me. You’re too distant in my memory, in the back of my mind that I’ve forgotten that you are a stranger. Do you still keep the letters I wrote for you?

In my head, you’re still my best friend but I’ve forgotten what your name is. You are nameless. Yet, I still remember the name of your favourite band. I still remember your height. You ran into the furthest back of my head, and that’s where my memory is at its best. If you ran this fast during PE, maybe you’d actually pass the 2.4 km run.

Have you been thinking of me? The love I’ve left, is it nameless like you? Perhaps, you’ve erased us from your memory because you have been acting like history had never existed. To be fair, you don’t even take History lessons. I do. Perhaps, it’s destiny for me to remember history better than anyone else. Better than you. The Vietname War, the Korean War, I was supposed to have it memorised by now. And yet, during history lessons, all I can think of is writing your name in place of the important figures of history.

How is your new friend? Has she been treating you well? I hope she has. Every time I glance at the both of you, I write every quadratic solution of yours into her skin. You really really liked math. You’d complain about how hard it was so I figured out the solution to form a heart on my graph paper. Because it reminds me of you. Although I was really bad at math. But now, her skin is full of my quadratic equations. For me. To forget. Every tiny bit of you. Every solution of us. Do you like my graphs? Like I said, It forms a heart. It’s now hers. 

Can I ask a simple question? What date is it today? Wait, its your birthday.

Happy birthday! Thank you for everything you’ve done for me, all your advice and support. I love you so so much. Let me just find my gift for you.

Wait, it’s my birthday today. Who’s birthday party is this then? Oh, mine? RIGHT IT IS MY BIRTHDAY. I WAS THE ONE WHO ORGANISED IT. But why are you here? Who are you and why were you invited?

What was your name again? Could you please introduce yourself?

[gemkun]

@luckquartzed said : “Negative b, plus or minus, the square root of b squared… minus 4ac over 2a…” Aventurine flips through the textbook and scoffs. “This is what they teach kids in school? Man, I’m glad I never went. How come there’s nothing in here about voting, opening a credit account, buying a house or first aid? Who thought this belonged in public academics instead of specialized university?” He drops the book in the trash. “What a waste of 500 credits.” “It’s all inductive anyways, can’t really prove anything, watch out for the giant teapot orbiting the sun. Also moons are all made of cheese.” Aven is just being an add at this point and he knows it. “How come no matter what colour the liquid, the froth is always white?”

      ⸻       this   was   to   be   absolutely   expected.   though   ,   it   is   not   the   fault   of   the   avgin   ,   but   rather   the   education   system   and   its   failure   to   indicate   applications   relevant   to   the   livelihoods   of   others.   ❝   it   is   one   aspect   ,   but   there   are   plenty   of   other   topics   that   are   covered   within   prescribed   syllabi.   ❞   he   eyes   the   discarded   purchase   —   identifying   the   precious   publication   being   laid   to   waste.

  still   ,   his   subsequent   reasoning   ,   borders   absurdity.   in   fact   ,   it   is   explicitly   nonsensical.   ❝   what   you   have   a   listed   are   essentials   ,   no   doubt   ,   but   you   severely   underestimate   the   capabilities   of   the   quadratic   formula.   ❞   outstretched   ,   he   is   thankful   that   the   fallen   text   is   not   marred   by   assorted   scraps   ,   and   for   that   ,   his   retrieval   follows.   he   dusts   it   then   ,   to   remedy   its   bruised   state   ,   before   he   passes   it   to   its   respective   owner   ,   both   former   and   returned.

  ❝   it   is   a   consolidation   that   allows   the   ability   to   solve   the   simplest   type   of   polynomial   equations   that   can   be   used   to   study   complex   systems   within   certain   limits.   they   appear   routinely   in   all   facets   of   mathematics   and   if   you   do   not   appreciate   this   formula   ,   you   will   surely   struggle   as   you   venture   further   into   arithmetic   problems.   ❞   flipping   open   the   educational   tool   ,   he   exposes   the   strategist   to   the   mediocre   explanation   across   glossy   pages.   to   assist   his   elaboration.   ❝   what   you   fail   to   comprehend   ,   is   this   concept   ,   is   applicable   to   countless   conditions   in   everyday   life   ,   including   your   dice   throws.   ❞

  and   perhaps   ,   one   he   employs   when   he   faces   these   roulettes   with   the   stoneheart.   ❝   in   its   most   basic   form   ,   it   determines   the   area   of   figures   —   by   expressing   the   area   with   a   quadratic   equation   ,   we   can   seamlessly   calculate   this   unknown.   if   we   take   this   further   ,   another   example   is   a   projectile   :   the   place   where   it   lands   ,   the   distance   travelled   and   the   time   it   takes   to   reach   its   vertex   can   be   established.   have   you   worked   out   its   use   yet   ?   ❞

  raised   brow   curls   ,   prompting   the   elite   in   a   manner   that   spells   ❛   this   should   be   obvious   ❜.   and   yet   ,   the   questions   persist   ,   coaxing   a   launch   of   spaced   out   sighs   ,   but   the   doctor   answers   nevertheless.   ❝   it   proves   plenty   ,   gambler.   i   should   assign   you   to   not   only   completing   this   section   in   your   book   ,   that   you   must   take   greater   care   of   ,   but   i   should   also   task   you   to   understand   its   application   in   your   daily   conventions.   ❞

  finality   falls   in   his   next   conviction   ,   with   piercing   gaze   to   deter   the   director   from   bothering   any   longer.   since   ,   well   ,   they   both   have   more   pressing   matters   to   attend.   ❝   to   correct   you   ,   not   all   foam   is   white.   however   ,   in   the   case   you   speak   of   ,   the   froth   is   white   due   to   light   refraction.   since   it   is   made   of   bubbles   ,   which   are   pockets   of   air   ,   light   that   enters   must   pass   through   a   number   of   surfaces   ,   which   scatter   it   in   different   directions   that   produces   this   white   colour.   ❞

  certainly   ,   this   must   sate   the   liquidation   specialist.   though   ,   if   not   ,   he   has   no   more   minutes   left   to   spare.

[shiri-shine]

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[ncogofficial]

Quantum-Secure Blockchain: Why Your Wallet Needs It NOW!

Blockchain networks implementing cryptographic methods to guard against quantum computing threats are referred to as Quantum-Secure Blockchain. Traditional blockchain networks utilize RSA (Rivest-Shamir-Adleman) and ECC (Elliptic Curve Cryptography) as their cryptographic mechanisms, but remain secure from classical computer attacks while remaining completely vulnerable to quantum-enabled Shor’s Algorithm. 

Shor’s Algorithm demonstrates formidable capabilities in factorizing vast numbers as well as conducting discrete logarithm calculations, which undermine existing blockchain network protection mechanisms. The progressive development of quantum computers creates vulnerable cryptographic systems through broken encryption, preventing blockchain security and protected information from remaining secure.

Quantum-Secure Blockchain implements cryptography from the quantum-resistant category that delivers an entire blockchain defense against attacks from quantum computers. Quantum-Secure Blockchain implements cryptographic techniques that exhibit quantum resistance instead of conventional methods that quantum attacks can penetrate. Three quantum-resistant cryptographic methods include lattice-based cryptography, hash-based cryptography, and multivariate quadratic equations.

Lattice-based cryptography, for example, is based on the hardness of solving problems in high-dimensional spaces for the same reason that attacks conventional encryption, to which quantum computers don’t seem to be able to do in an uncomplicated manner. Hash-based cryptography is based on the hash function being secure, and multivariate quadratic equations involve mathematical computations that are difficult for quantum computers to solve efficiently. 

Through the implementation of these innovative methods, quantum Secure Blockchain makes sure that even when the quantum computers have reached their fullest development, they won’t be able to breach the cryptographic security of the system.

The most important things about Quantum-Secure Blockchain are beyond the fact that it makes use of quantum-resistant algorithms. One of the key characteristics of Quantum-Secure Blockchain is that it employs bigger key sizes and more intricate mathematical bases than conventional blockchain systems. Quantum computers, which can perform enormous amounts of data in parallel, can take advantage of smaller key sizes and less complex mathematical issues much more efficiently than traditional computers. 

Using bigger keys and more challenging mathematical hurdles, Quantum-Secure Blockchain keeps quantum computers at bay and ensures that neither can break into the encryption quite so readily. This additional layer of cryptographic strength makes Quantum-Secure Blockchain extremely resistant to attacks by quantum devices, protecting blockchain transactions and data in a fashion that ordinary cryptographical processes simply can’t match.

Another crucial aspect of Quantum-Secure Blockchain is that it employs post-quantum cryptography and forward secrecy protocols. Forward secrecy assures that even if one’s cryptographic key gets compromised in the future, historical communications and transactions are safe. This becomes particularly relevant in terms of quantum computers because quantum computers might decrypt archived data in the future. 

Through applying post-quantum cryptography protocols, Quantum-Secure Blockchain can safeguard not only future data but even past data in a manner such that data placed on the blockchain is impenetrable even if today’s data were intercepted and broken at some later date. With proactive security, it pre-protects blockchain networks from the increasing capabilities of quantum computing.

The vision of Quantum-Secure Blockchain is to anticipate and pre-empt the security threat represented by quantum computers before this can materialize into a genuine danger. By implementing quantum-resistant cryptography now, Quantum-Secure Blockchain creates an essential layer of protection that resists sensitive information against the unforeseen capacity of quantum computers. 

The continuous development of quantum computing poses a constantly changing threat to cybersecurity, but Quantum-Secure Blockchain is designed with foresight and ingenuity to remain ahead of the curve. It is not only concerned with the present situation of cryptographic attacks, but also thinking ahead to developing blockchain systems for the future when quantum computers can potentially decrypt conventional encryption algorithms with ease.

By tackling such challenges head-on, Quantum-Secure Blockchain enables blockchain technology as a secure and reliable platform for digital transactions despite the advent of quantum computing. The more superior and powerful that quantum computers will become, the more critical will be Quantum-Secure Blockchain. 

Not only is it theoretically imperative to transition to quantum-secure encryption methods, but an urgent imperative, as the future of blockchain hangs in the balance of quantum defense against attack. Quantum-Secure Blockchain, with its robust cryptographic processes and innovative thinking, provides the security needed to maintain the integrity of blockchain systems against impending quantum attacks.

Quantum Computing vs. Blockchain: The Security Solution

The connection between blockchain and quantum computing is that of danger and potential boon. The stupendous amount of computational power available with quantum computing would completely upset blockchain technology by breaking the very cryptography algorithms underpinning it. Blockchain relies strongly on asymmetric cryptography, which, as secure against traditional computers as it currently is, would be vulnerable to the sophisticated algorithms quantum computers would employ, specifically Shor’s algorithm. 

Such an algorithm can potentially factor large numbers quickly and accurately, undermining RSA and elliptic curve cryptography (ECC) that protects blockchain transactions today. But this weakens it yet. Quantum-Secure Blockchain is a promising resolution that can secure the guarantee of continued safety and reliability of blockchain against quantum threats.

Asymmetric cryptography stands as the core protection mechanism of blockchain security because public and private keys enable encryption and decryption functions. Traditional computers encounter great computational challenges when attempting to either factorize large numbers or determine discrete logarithms. 

Quantum computers, which employ the principles of quantum mechanics, can accomplish this exponentially quicker, hence rendering current encryption outdated. This is where the real adversarial potential of blockchain and quantum computing comes into play. If quantum computers advance to a point, they can potentially undermine blockchain security by decrypting encrypted data and manipulating transactions, exposing blockchain networks to attack.

But Quantum-Secure Blockchain reverses this script. Instead of simply falling victim to the potential threat of quantum computing, Quantum-Secure Blockchain has been designed specifically to resist such future attacks. The cryptographic approach of Quantum-Secure Blockchain offers security by resisting all potential unauthorized access from quantum computers that might break standard encryption. 

The secure quantum-resistant algorithms use mathematical challenges that quantum computers cannot easily resolve through three types of cryptography: lattice-based, hash-based signatures, and code-based. Through the incorporation of these new strategies, Quantum-Secure Blockchain allows blockchain systems to remain resolute, maintaining their fundamental purpose of offering secure, transparent, and decentralized transactions.

Transition to Quantum-Secure Blockchain is not an anticipatory measure, but it is unavoidable. Blockchain’s application of asymmetric cryptography is its weak point in the event of quantum computing. Existing cryptographic infrastructures might be sufficient to provide sufficient security against attacks based on classical computation, but they are no match for the brute force processing capability of quantum computers. 

Quantum-Secure Blockchain has never been more necessary, since quantum computers continue to move closer to being powerful enough to decrypt the methods used to safeguard digital transactions for decades. Therefore, Quantum-Secure Blockchain is not merely a future upgrade to be done optionally; it is the new standard that blockchain networks will have to adopt to survive in the post-quantum era.

The quantum computing threat to making blockchain susceptible exists, but now with the emergence of Quantum-Secure Blockchain, there is a simple answer. Using proper cryptographic techniques, blockchain networks will be able to survive even in the quantum era. Developing and using Quantum-Secure Blockchain is needed to make sure blockchain networks will withstand the brunt of heavy quantum computing attacks looming on the horizon. 

The ongoing expansion and deployment of blockchain across sectors like finance, healthcare, and government necessitate the level of vision that Quantum-Secure Blockchain provides. Besides averting quantum attacks from undermining data integrity, it also guarantees the long-term sustainability of blockchain technology in securing transactions and establishing trust within industries.

The development path of quantum computing requires quantum-secure blockchain to secure blockchain systems from threats generated by the emerging computational strength. The Quantum-Secure Blockchain solution shows how to create blockchain networks with modern quantum attacks prevention while maintaining complete security principles. With the advent of quantum-resistant algorithms, Quantum-Secure Blockchain guarantees that blockchain will continue to be the linchpin of secure digital transactions and is a primary solution to the problem of quantum computing.

Quantum-Secure Blockchain is not only a security measure for blockchain against quantum computing, but also charts the future of blockchain in itself. Global infrastructure growth of blockchain networks creates a stronger demand for Quantum-Secure Blockchain technologies. 

The lack of Quantum-Secure Blockchain would make blockchain networks susceptible to quantum-based attacks, so that trust in decentralized systems would decrease. However, with Quantum-Secure Blockchain, blockchain can be designed to address the needs of a quantum-energy-rich world, such that its authenticity is guaranteed through the next century.

The emergence of quantum computing is a threat and a prospect to blockchain technology. Quantum computers are not only capable of deciphering the cryptographic methods used to protect blockchain transactions, but Quantum-Secure Blockchain presents a pre-emptive strike in proposing quantum-resistant encryption techniques. Asymmetric cryptography for blockchain is a vulnerability that needs to be eliminated, and blockchain security’s future rests on Quantum-Secure Blockchain. 

The normal practice of the future will be Quantum-Secure Blockchain because it protects blockchain from quantum attacks while ensuring its operation during such potential threats. Through the implementation of Quantum-Secure Blockchain, organizations can protect blockchain technology as an essential secure digital transaction solution even after quantum computers become operational.

Why Quantum-Secure Blockchain is Essential for Crypto Survival

Cryptocurrency remains in an important stage of development because its global market value exceeds $2 trillion. The market has grown to an enormous size and adoption, but it also has enormous problems to solve. Of particular concern is the quantum threat. While traditional blockchains such as Bitcoin and Ethereum are secure against vanilla computers, they are not secure against quantum attacks by design. 

As quantum computers are developing, they may be able to break through the cryptographic technologies that secure blockchains today. Unless something is done in advance, the prospects of cryptocurrencies become doubtful, and Quantum-Secure Blockchain...

[tuulikki]

The further back these concepts came from in time, the more they were part of a chain of knowledge transmission across vast distances and centuries in which the provenance (or “discovery”) was easily lost. And a lot of these things were “discovered” at different times in different places.

Just to give the quadratic equation as an example, al-Khwarizmi didn’t invent the equation you studied in school. He inherited a tradition of development—and it went on to be further developed for centuries after his death until we eventually got the quadratic equation we got today. It’d be like saying the Mexicans invented pizza because they were the first to combine tomatoes and carbohydrates.

And definitely everyone doing the “history written by the victors” stuff in the notes is overlooking the fact that no Europeans showed up in 7th-century India to loot books on mathematics.

It’s important to differentiate between theft and sharing. Imperialism was a specific evil and we need to use that word accurately to not dilute it. We have legal distinctions between manslaughter (accidental) and murder (intentional) for a reason: intention matters.

Calling everything imperialism lets Europeans off the hook by creating this idea that an imperial mindset was some eternal innate European quality. It wasn’t. There were specific choices made, with a whole intellectual system of pseudo-logic to justify it and infrastructure deliberately built to enforce it.

Here's the link to the video

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[authorjond369]

❖ Solving Quadratic Equations by Factoring - Basic Examples ❖

Solving Quadratic Equations by Factoring – Basic Examples. In this video, I solve two basic quadratic equations by factoring. Notice that the second quadratic equation is a bit more tricky, largely due to the coefficient in front of the x^2 term. To factor this quadratic polynomial, I simply use trial and error and then check my work to be sure that I have factored correctly.In this video I also…

[sathcreation]

Expert IIT Mathematics Teacher at Gritty Tech

Introduction to IIT JEE Mathematics Excellence

The journey to cracking the prestigious IIT JEE begins with mastering one of its most challenging components – Mathematics. At Gritty Tech, we understand the intensity and depth required to succeed in this subject. That's why we offer specialized coaching under the guidance of expert IIT Mathematics teachers who not only know the syllabus but also understand the psychology and strategy behind high-stakes exams For More…

Our teaching is not just about covering topics. It’s about building a solid mathematical foundation, developing analytical thinking, and fostering a problem-solving mindset.

Why Expert Teachers Make a Difference

IIT JEE Mathematics is not about rote learning. It demands creativity, speed, accuracy, and deep conceptual understanding. An expert IIT Maths teacher brings all these elements to the table. At Gritty Tech, our instructors are selected through a rigorous process. Each of them has years of experience in mentoring toppers, with proven results across multiple batches.

Key Attributes of Our Expert Maths Faculty:

In-depth Subject Knowledge: Every teacher at Gritty Tech has a mastery over the entire JEE syllabus including Algebra, Calculus, Coordinate Geometry, Trigonometry, Probability, and more.

Strategic Teaching Methods: They know how to break down complex problems into simpler steps and highlight shortcuts that save time in exams.

Focus on Conceptual Clarity: Instead of encouraging memorization, our approach ensures students understand the 'why' behind every formula.

Real Exam Insight: Teachers share insights from previous year papers, trends, and changing patterns in JEE to keep students one step ahead.

Individual Mentorship: Every student is different. Our experts provide personal guidance to overcome weaknesses and build on strengths.

A Curriculum Built for Success

At Gritty Tech, the Mathematics curriculum is not generic. It is crafted specifically for IIT JEE aspirants, keeping in mind the latest trends, difficulty levels, and expected question formats. Our curriculum is reviewed and refined every year by a panel of experts.

The Core Topics Covered Include:

Algebra: Quadratic equations, Complex numbers, Matrices & Determinants, Permutations & Combinations

Calculus: Limits, Continuity, Differentiability, Application of Derivatives, Integrals, Differential Equations

Coordinate Geometry: Straight lines, Circles, Conic Sections

Trigonometry: Identities, Equations, Inverse Trigonometric Functions

Vectors and 3D Geometry

Probability and Statistics

Each topic is taught from the ground up, beginning with theory and moving into solved examples, practice sheets, test series, and revision strategies.

Teaching Methodology at Gritty Tech

What truly sets Gritty Tech apart is not just the content we teach, but how we teach it.

Interactive Concept Classes

Our sessions are designed to be interactive. Teachers use smart boards, real-life analogies, and visual aids to explain abstract mathematical ideas. Every class ends with a set of practice problems that help reinforce the day’s learning.

Doubt Resolution in Real-Time

Students never have to wait till the end of the week to clear their doubts. With dedicated doubt-solving sessions and availability of the faculty even outside class hours, learning continues seamlessly.

Regular Testing and Feedback

Frequent quizzes, weekly tests, and full-length mock exams are conducted to ensure students are exam-ready. After each test, teachers provide personalized feedback and performance analysis.

Adaptive Learning

Not every student learns the same way. Our experts use adaptive learning techniques to identify the learning style of each student and modify their approach accordingly.

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Maths Assignment Support in the UK: Solving Complex Quadratic Inequalities

Struggling with mathematics assignments in the United Kingdom? Finding authentic mathematics assignment help in UK services is essential if you want to achieve success academically. Since there are many choices available online, it is essential to assess these services so you get the quality work that you expect.

This blog has presented how you can assure quality services and how Locus Assignment offers best-in-class solutions specifically suited to you.

Why Is Verification Important?

Verification is essential before you give any platform any assignment. It saves you time, and effort, poor quality work, protects your money, maintains the level, and finally gets you quality grades. Don't get trapped by those giving you plenty but delivering nothing.

Key Quality Indicators

When selecting maths assignment assistance in the UK, bear these issues in mind:

Qualified Experts: Choose services that employ experts qualified in your specialized mathematics discipline. Experienced experts handle complex problems well.

Plagiarism-Free Content: Priority Is Given to Original Work. The service guarantees 100% original content.

Samples: Reputable agencies tend to offer samples, indicating the quality of work.

Timely Delivery: Timely submissions are essential. Check the track record of the service regarding on-time delivery.

Customer Feedback: Read other students' reviews and ratings. Positive reviews are an excellent measure of dependability.

Transparent Pricing: Clear price models that contain no added fees.

24/7 Support: Support twenty-four hours, seven days per week.

Locus Assignment provides quality and reliable assignment assistance with mathematics assignments in the United Kingdom. Simply provide the assignment details, and the experts will provide support.

Key Benefits of  Our Services

Choosing a certified supplier has several advantages:

Accurate Solutions: Precise platforms offer accurate solutions to complex problems, empowering you to achieve.

Time Management: Reclaim time by leaving it to the experts.

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Customized Support: Personalized support aligns their work specifically to your requirements.

Why Choose Locus Assignment?

Locus Assignment is one of the best mathematics assignment helpers, cognisant of the issues facing students. Why are we best suited?

Experienced Math Specialists: Our experienced team includes assignment assistants UK with vast expertise across many areas of mathematics.

Plagiarism-Free Guarantee: We guarantee 100% original content, with all assignments undergoing rigorous plagiarism checks.

Timely Delivery: Timely delivery comes first, while quality comes next.

Budget-Friendly Plans: Economical plans suited to the financial ability of every student.

24/7 Support: At any time, there is always an available support team.

Solving Quadratic Inequalities Quick Reference

Quadratic inequalities are comparisons of an inequality term, normally zero, and a quadratic expression. An overview follows below.

Standard Form:

 Rewrite the inequality in standard form: ax² + bx + c > 0 (or <, ≤, ≥).

Find the Roots: 

Find the solution by solving the equation associated with the form ax² + bx + c = 0. Example: Find x if x² - 5x + 6 < 0. By factorization, (x-2)(x-3) = 0, so x = 2, x = 3.

Test Intervals: The number line is divided by the roots. 

Choose one test value from each interval. Example: Intervals are (–∞, 2), (2, 3), (3, ∞). Choose x = 1, x = 2.5, x = 4.

Determine Solution: By substituting values, find values that satisfy the inequality. Example: x = 1 (False), x = 2.5 (True), x = 4 (False). Write Solution: Represent the solution in the form of an interval. Example: Solution to x² - 5x + 6 < 0 is (2, 3). 

Conclusion 

Don't let mathematics assignments get you down. Locus Assignment has expert mathematics assignment help in the UK, providing guidance, time management, and personal support. Mathematics Assignment Assistants will provide you with the authority to complete assignments efficiently and build confidence. Upload an assignment today and attain success.

[futuristicinno]

How to Solve Quadratic Equations: 5 Simple Methods with Examples Quadratic equations might seem intimidating at first, but once you understand the different solving methods, they become much easier to handle. Whether you're a Class Read more

[geniustut]

The Integrated Program in Management Aptitude Test (IPMAT) is a highly competitive exam that requires thorough preparation, particularly in the Quantitative Aptitude section. This section assesses a student’s problem-solving skills, mathematical proficiency, and logical reasoning abilities. Many aspirants seek the best coaching for IPMAT in Delhi to enhance their preparation and improve their chances of success.

Why is Quantitative Aptitude Important in IPMAT?

Quantitative Aptitude is a crucial part of the IPMAT exam as it evaluates a candidate’s ability to handle numerical and analytical problems. A strong foundation in this section can significantly impact overall performance. For this reason, enrolling in IPMAT coaching online in Delhi can provide structured learning and expert guidance to tackle this challenging section effectively.

How Coaching Helps in Mastering Quantitative Aptitude

1. Structured Learning Approach

One of the key advantages of joining the best online coaching for IPMAT in Delhi is the systematic and structured learning approach. Coaching centers divide the syllabus into smaller topics, allowing students to focus on each concept separately. This ensures a better understanding and gradual progression in complexity.

2. Expert Guidance and Teaching Methods

Coaching institutes provide experienced faculty who specialize in IPMAT preparation. Through IPMAT preparation coaching in Delhi, students receive expert mentorship that helps them grasp mathematical concepts efficiently. Faculty members use real-world examples and problem-solving techniques that make learning engaging and effective.

3. Regular Practice and Mock Tests

Frequent practice is essential for mastering Quantitative Aptitude. Enrolling in an IPMAT online course in Delhi provides students access to numerous mock tests and practice papers that simulate the actual exam environment. Regular tests help in improving speed, accuracy, and time management, which are critical for this section.

4. Concept Clarity with Doubt-Solving Sessions

Many students struggle with difficult topics like Algebra, Probability, and Number System. IPMAT online coaching in Delhi offers doubt-solving sessions where students can get their queries addressed by experts. This enhances conceptual clarity and boosts confidence in problem-solving.

5. Personalized Learning Experience

One of the benefits of IPMAT coaching near me in Delhi is that coaching institutes provide customized learning plans based on individual student strengths and weaknesses. Online coaching platforms analyze performance and suggest specific areas for improvement, ensuring that students get the most out of their preparation.

Key Quantitative Aptitude Topics Covered in IPMAT Coaching

1. Arithmetic

Profit & Loss

Percentages

Time, Speed, and Distance

Simple and Compound Interest

2. Algebra

Quadratic Equations

Linear Equations

Polynomials

Functions and Graphs

3. Number System

Divisibility Rules

Factors and Multiples

HCF and LCM

4. Geometry and Mensuration

Properties of Triangles

Circles

Volume and Surface Area

5. Probability and Statistics

Basic Probability Concepts

Mean, Median, and Mode

Permutations and Combinations

How to Choose the Best IPMAT Coaching?

When searching for IPMAT classes near me in Delhi, students must consider factors such as faculty experience, study material quality, and student support services. Here are some key aspects to look for:

Qualified Faculty: Ensure the coaching institute has experienced instructors who specialize in IPMAT preparation.

Comprehensive Study Material: The best coaching institutes offer updated notes, question banks, and reference materials.

Mock Tests and Performance Analysis: Regular assessments help track progress and improve weak areas.

Flexible Learning Options: Many students prefer IPMAT coaching online in Delhi for convenience and flexibility.

Advantages of IPMAT Online Coaching in Delhi

1. Learn Anytime, Anywhere

With online coaching, students can attend classes from the comfort of their homes, eliminating travel time. This makes it a convenient option for those looking for IPMAT preparation coaching in Delhi with flexible learning schedules.

2. Access to Recorded Lectures

Online coaching platforms provide recorded lectures that students can revisit anytime. This helps in revising difficult topics and reinforcing learning.

3. Interactive Learning Environment

Many online coaching programs include live interactive sessions where students can participate in discussions and ask doubts in real-time, making learning more engaging.

4. Cost-Effective Learning

Compared to traditional classroom coaching, IPMAT online coaching in Delhi is often more affordable while providing high-quality education and resources.

Conclusion

The Quantitative Aptitude section of IPMAT requires focused preparation and strategic learning. By enrolling in the best coaching for IPMAT in Delhi, students gain access to expert guidance, structured study plans, and extensive practice material. Whether you choose classroom learning or opt for an IPMAT online course in Delhi, selecting the right coaching institute is crucial for success.

Investing in IPMAT coaching near me in Delhi can significantly improve mathematical proficiency, boost confidence, and enhance overall performance in the exam. Choose the best coaching option that suits your learning style and start your journey towards IIM success today!

Originally published at https://www.geniustut.com on March 6, 2025.

[360asvab-tutoring]

Mastering Mathematics Knowledge For ASVAB TEST

The Mathematics Knowledge section tests your understanding of algebra, geometry, and basic number theory. Linear Equations: Solve for the unknown variable in simple equations. Example: 3x + 5 = 20. Solve for x. Solution: Subtract 5 from both sides → 3x = 15 → x = 5. Solving Inequalities: Similar to solving equations, but with greater than or less than signs. Example: 2x + 4 > 10 → 2x > 6 → x > 3. Quadratic Equations: Use factoring, completing the square, or the quadratic formula to solve. Example: Solve x² - 6x + 9 = 0.Solution: (x - 3)(x - 3) = 0 → x = 3.

Get more practice lesson and study materials on ASVAB Tutoring , also you can go for online practice test. 👈