Examples: A Different Way to Solve Quadratic Equations

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4 жыл бұрын

If you'd like to continue learning in this style, Prof. Loh runs a systematic course series which focuses on teaching people how to invent their own mathematical techniques (live.poshenloh.com/), as well as regular streams on this KZfaq channel.
Want to understand how to solve any quadratic equation, without just memorizing the quadratic formula? In this lesson full of worked examples, Daily Challenge founder, Carnegie Mellon University professor, and U.S. International Math Olympiad coach Po-Shen Loh introduces a simple, different method for solving quadratic equations. Instead of guess-and-check, this method uses students’ existing experience searching for a pair of numbers with a given sum and product to solve quadratics.
This video explains all of the details behind Prof. Loh's initial quadratic method video (kzfaq.info/sun/PLqv4sKOD1b..., including different examples of how to use the method to solve more and more general quadratic equations.
Prof. Loh came to discover this method because he has been systematically thinking about how to explain school math concepts in more thoughtful and interesting ways, while creating lessons for our Daily Challenge (live.poshenloh.com/).
Thanks to the Templeton World Charity Foundation for their support of this work.
==========
UNIQUE APPLICATIONS OF THE METHOD
Looking for a specific kind of problem that this method can solve? Check out the timestamps below:
21:24 Coefficients with different signs
25:03 If the coefficient of x is odd
27:28 If x² has a coefficient other than 1
30:41 Deriving a Quadratic Formula
33:14 Deriving the commonly learned Quadratic Formula
HISTORICAL PARTS OF THE SOLUTION
38:18 Viète’s Relations
39:00 Babylonian Mathematics
==========
ABOUT DAILY CHALLENGE
The Daily Challenge with Po-Shen Loh is a series of online math courses designed to teach people how to invent, taught by an actual inventor. The novel teaching style continually presents students with problems that they barely don't know how to solve, and guides them to invent their own solution methods through hints. It covers a wide range of ability levels, starting from basics which only require Pre-Algebra, and reaching up to university-level topics such as Number Theory. Instead of simply teaching the standard curriculum earlier, it goes deeper, providing additional challenges outside of the classroom. The course series also provides an efficient way to systematically cover math competition topics. To learn more about Daily Challenge with Po-Shen Loh, visit daily.poshenloh.com.
ABOUT EXPII
Expii is a free math and science education platform that embraces what makes us all individuals: our voices, experiences, and cultures. We encourage choice and experimentation by giving students the power to choose how they learn. Through creative, fun, practical, and personal lessons each person can have their own aha moment.
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If you have a middle schooler who is interested in thinking deeper about math, join our biweekly newsletter to learn more about math competition information, education news, and the inside scoop on all things Daily Challenge with Po-Shen Loh. Subscribe now by visiting www.eepurl.com/gExYzT.

Пікірлер: 1 500

@BravoTango-vt8em 4 жыл бұрын

This is the type of math teacher I like. The teacher who actually lets their kids understand the math instead of making them pass the exam so he doesn’t have to worry about it again.

@muhammadazeem9775 4 жыл бұрын

kzfaq.info/get/bejne/gpp5oNx305fcfJ8.html

@ashishkushwaha2214 3 жыл бұрын

Right bro

@aravinds3846 3 жыл бұрын

I wish I saw this lecture before JEE exam lol. The graph method makes the questions INCREDIBLY easy

@ooffoo5130 3 жыл бұрын

he also has an iq of like 230 so that might have something to do with it

@antoniofuller2331 3 жыл бұрын

Hmm

@robertmcfarlane8546 4 жыл бұрын

This is one of the best lectures on quadratic equations I have seen. Thank you Mr Loh for clear and understandable information presented in a concise manner.

@psloh 4 жыл бұрын

Thanks for your feedback!

@Morningstarintheroses 4 жыл бұрын

@@psloh sir, could you please reply me??

@muhammadazeem9775 4 жыл бұрын

kzfaq.info/get/bejne/gpp5oNx305fcfJ8.html

@d.chandrasekara7959 2 жыл бұрын

Why 14 doesn't become -14 as in x^2-14x+24, can someone explain it pl

@jimspelman8538 3 жыл бұрын

I am a math and computer science major and a math teacher (middle school) and, like others have commented, I have never seen this method before. I love how you can easily get non-integer solution sets! Perhaps instead of the "Po-Shen Method" I shall henceforth call this the "Magic Quadratic Po-Shen" (just to add a little wordplay)!

@chocolateangel8743 3 жыл бұрын

I saw a video in which a college professor did the same thing -- because he couldn't remember how to pronounce his name.

@Tweeting_data Жыл бұрын

Portion

@rajeevmaakan1347 4 жыл бұрын

I salute you man! This is absolutely amazing....have been teaching math for 35 years, you have just made my job easier for whatever remaining number of years I will be able to teach. That's why they say....it doesn't matter you learned something new so late in life, what matters is you got new knowledge (new, I say, for the learner), new wisdom. And last but not the least, what is the primary objective of Problem solving....in any branch of knowledge or education....it is to achieve the objective in as simple and as uncomplicated a manner as possible....so that it can bring a smile on the faces of our students. Thanks a zillion bro!!!

@User00159 Жыл бұрын

Sir pls do research on vedic maths which will change your life 🇮🇳🇮🇳

@RavinaTutorial 4 жыл бұрын

Sir please keep posting such methods so that people start analyzing mathematics and taste the true essence of it, Thank you so much for sharing this🙏.

@psloh 4 жыл бұрын

@tamajongmichaelnkeh1978 4 жыл бұрын

That is the easiest method I have ever used. I can't imagine that I did not know this before. Thank you sir

@luzianleser 4 жыл бұрын

Google PQ

@DominicanOps 4 жыл бұрын

I think the Colombian Method is easier to be honest.

4 жыл бұрын

DominicanOps what Is the colombian method?

@user-wq7dv3vs3p 4 жыл бұрын

@ kzfaq.info/get/bejne/oMmCipWDmZjFqnk.html

@theunseenblade5897 4 жыл бұрын

kzfaq.info/get/bejne/qriSn9qF2L6amIU.html KZfaqrs discovered it years ago

@geraldillo 4 жыл бұрын

Every highschool teacher should learn this method

@rukmaniranganathan8420 4 жыл бұрын

Yes

@daisygacha311 4 жыл бұрын

True talk

@muhammadazeem9775 4 жыл бұрын

kzfaq.info/get/bejne/gpp5oNx305fcfJ8.html

@chandasubba3502 4 жыл бұрын

X²+6x-27=0

@devonyumen8116 3 жыл бұрын

No plssss. This is complicated 😭😭 like why can't we just use the quadractic formula. It isn't that difficult to remember 😔

@beteilniguse8072 4 жыл бұрын

This is exactly how we learned in my country East Africa. God how did I forget this, and our professor has zero clue and got me confused and spent days to really figure this out. I wish I found you early. I would have saved a lot of time. But thank you so much! You did an amazing job. keep them coming.

@harisomerbasic9136 4 жыл бұрын

My teacher had me explain this to her and now she's recommending your technique and referencing to you! Thanks from Sweden!

@harisomerbasic9136 4 жыл бұрын

not your but as a tip

@jackeroo75 4 жыл бұрын

Of course other countries know this while USA still wants kids to learn the route method

@muhammadazeem9775 4 жыл бұрын

kzfaq.info/get/bejne/gpp5oNx305fcfJ8.html

@LiveHappy76 2 жыл бұрын

@@muhammadazeem9775 Just a tip, based on my personal preference. I almost never click on a video link that does not include a brief statement of what the content/summary of that video is...you'll attract more clicks with a brief statement. Nice rose picture.

@norbertotorbeso2562 4 жыл бұрын

I have been teaching this method to my high school students back in 1999 and yes, this is another way. Students will definitely learn if a teacher will expose them to different ways of solving the problem. Nice presentation...

@geraldillo 4 жыл бұрын

I realise that this is basically not much different than completing the square. Why was this method not widespread before? It would have saved many students a whole lot of suffering...

@Latronibus Жыл бұрын

@@geraldillo The one thing I don't like about this method relative to completing the square is that it doesn't teach the "add and subtract" trick, which is useful elsewhere in math. To clarify what I mean, I think of completing the square in this kind of format: x^2+2x+2=x^2+2x+1-1+2=(x+1)^2+1. The "I can just put a +1 there as long as I take it away later" concept is kind of magical to an algebra student, but is widely used elsewhere in math. Unfortunately I sometimes see students learning this in terms of adding the desired quantity to both sides of an *equation* which is really the less common way to think about it in more advanced math.

@espenvang3053 4 жыл бұрын

What a marvellous lecture in every way! Not just a genius new method for solving quadratic equations, but also clear and precisely presented.

@fyradur 4 жыл бұрын

Damn I've never been able to solve quadratic equations with irrational solutions purely in my head but now I can.

@aaditrangnekar 2 жыл бұрын

Do your work and find some podophiles not quadratic lol

@part4963 2 жыл бұрын

@@aaditrangnekar lmao

@gautamghaisas 2 жыл бұрын

I wish we could have learnt all subjects this way in school. So systematically and brilliantly explained

@g.v.3493 4 жыл бұрын

I’m reviewing all of my precalculus math that I had 50 years (!) ago. I wish I’d had you for a math teacher back then. Thank you so much for the teaching an old dog a new trick! I’m planning to learn a lot more new tricks. I’ll be watching more of your videos in the future! Thanks so much!!

@blockyboxhead Жыл бұрын

I watched this entire video without getting bored or wanting to click off. This proves that this video is godly

@dananewborn8926 2 жыл бұрын

Thank you from my 19 person math class who enjoyed learning this method

@heaslyben Жыл бұрын

What a joy that this method fits naturally in each number domain! The intuition of "finding the average" leads so smoothly into creating a complex conjugate pair. It's as if we knew more than we knew we knew, all along. Thanks for sharing this so well!

@keinKlarname 4 жыл бұрын

You're such a friendly person! It's a pleasure to follow your explanations, Mr. Loh.

@trudyandgeorge 4 жыл бұрын

This is so elegant, intuitive, and forces the solver to think about what's happening and how things relate to each other. I wish I had KZfaq back when I was in school.

@gregnixon1296 4 жыл бұрын

If there were KZfaq when I was in school, I would never have gone to school. Attendance and tuition would have been a waste of resources.

@carolinebrown7634 3 жыл бұрын

VIO stand your life.

@ksamsati5254 4 жыл бұрын

What clarity, elegance & humility. Thank you.

@muhammedshameel5684 4 жыл бұрын

This is why I love mathematics, 😀😀

@muhammadazeem9775 4 жыл бұрын

kzfaq.info/get/bejne/gpp5oNx305fcfJ8.html

@joebrinson5040 4 жыл бұрын

I have never seen this method. Beautiful. Thank you. Retired math teacher.

@psloh 4 жыл бұрын

Thank you for your career of teaching!

@muhammadazeem9775 4 жыл бұрын

kzfaq.info/get/bejne/gpp5oNx305fcfJ8.html

@jecelaguilar9319 3 жыл бұрын

Haven't you taught your students one of the methods in finding for the roots of a quadratic equations is by completing the perfect square trinomial? This method is used how we arrived at the so-called quadratic formula😀

@chocolateangel8743 3 жыл бұрын

@@jecelaguilar9319 At first, I didn't get what he was doing. So, I Completed The Square on a couple of problems, using an area model. I'm a really visual and conceptual math learner, so things like area models really help me. After I did some problems, I realized that his method is basically a shortcut for Completing The Square. I had the idea because he said his method always works. To those of us in the U.S., this approach seems different because it's not the exact way we are taught to Complete The Square in school.

@MichaelBuck 2 жыл бұрын

Mind Blown! Genious! Not just in the solution but in the expert EXPLAINATION, very clear and understandable, just amazing! Thank you for taking the time to produce this video. I will go over it several times to make sure I understand its simplicity. I am now a follower and will look over your other videos. Wow, just amazing how ancient secrets from hundreds and thousands of years ago are lost over time but come back to life. I wonder how many other things are like this?

@sandanadurair5862 2 жыл бұрын

You are simply great. I have never seen such a pleasant mathematics teacher during my learning period. I am now 72. Today you taught me a novel technique. I salute you

@odinmandu2184 4 жыл бұрын

What have I been learning all my life🙆🏾‍♀️🙆🏾‍♀️ This is beautiful 🔥🔥🔥

@kirilkirilov6241 4 жыл бұрын

Great method! It's so rare you see an improvement over such a basic thing as quadratic equations. I just love your enthusiasm. Science Alert brought me here.

@philplante6524 Жыл бұрын

The method at 00:46 is just the quadratic formula. - B/2A +- u, where u^2 = B^2/4 - AC. The x-coordinate of the vertex of a parabola is -B/2A. It is also the line of symmetry. If you extend the line of symmetry through the x-axis, you will see that one root is a distance SQRT(B^2 - 4AC) to the right and the other is a distance -SQRT(B^2 - 4AC) to the left. The method is a bit different than just plugging numbers into the quadratic formula, but there is really no new math here, just a different way to apply the quadratic formula.

@mohamedabdou-salami 10 ай бұрын

No new maths but simpler maths 😊

@nicolealfonso5225 4 жыл бұрын

Thank you so much! I'm studying for the GMAT right now and this method is going to help me work through quant problems involving quadratic equations much more quickly and efficiently!!

@explorer2645 4 жыл бұрын

Brilliant! Very well explained. I wasn’t aware of this technique before...something different.

@alifmusyaffa9666 2 жыл бұрын

I can't believe that im finished watching this video, its amazing how Mr. PO makes math looks very interesting. Respect ❤️

@edlopez5661 4 жыл бұрын

What a great explanation to the how they came up with the quadratic equation. That was the best I've seen in quite a while. Thanks.

@alisharif3827 3 жыл бұрын

Thank you for your fantastic teaching skills. I'm very happy with your lessons, because it's so easy, but I don't know why they don't teach us in College like this beautiful way. Thanks a lot.

@johankotze42 4 жыл бұрын

Dear Prof Loh, I am now retired at 61, and I have worked in IT for most of my working life. I have, however, always dabbled in mathematics. The thrill of discovering this only recently, is one the reasons for my continued love of the subject. If you have not done so, adding the graphical interpretation would help many other students. Thank you very much.

@southernkatrina8161 4 жыл бұрын

Could we try it on Desmos?

@johankotze42 4 жыл бұрын

@@southernkatrina8161 Desmos?

@southernkatrina8161 4 жыл бұрын

Desmos is a free download app that takes a function and graphs it. It's good fun and helps learning.

@chocolateangel8743 3 жыл бұрын

I had to find videos that explained it, graphically, in order to fully understand what was going on.

@adamholub6436 4 жыл бұрын

I am from Czech republic and I know this since elementary school. It's one of the taught methods to solve cuadratic ecuations.

@samvendetta1744 3 жыл бұрын

Same in Kenya

@SuccessTeamEngineeringDesign 4 жыл бұрын

This is very helpful. Thank you Dr. Po Shen Loh for expounding our knowledge of maths in a precise way of Reasoning without guessing.

@edmund6392 3 жыл бұрын

Showed this to my 7 year old math obsessed daughter and she immediately understood. She loves learning advanced math and we love your explanations. Thank you!

@KarmaIsEternal 4 жыл бұрын

This man is a LEGEND!

@creativeclub2023 4 жыл бұрын

The Indian mathematician Brahmagupta (597-668 AD) explicitly described the quadratic formula in his treatise Brāhmasphuṭasiddhānta published in 628 AD,[24] but written in words instead of symbols.[25] His solution of the quadratic equation ax2 + bx = c was as follows: "To the absolute number multiplied by four times the [coefficient of the] square, add the square of the [coefficient of the] middle term; the square root of the same, less the [coefficient of the] middle term, being divided by twice the [coefficient of the] square is the value."

@zykorplayz7618 3 жыл бұрын

@@creativeclub2023 stfu

@-unnamed-2652 3 жыл бұрын

This is actually the pq-Formula, but i never understood how it came to live. Thank you for this illuminating explaination.

@raselalafaele4527 3 жыл бұрын

thanks Po-Shen Loh, I never studied this method in school or in University but I'm so thankful for sharing your knowledge and understanding of different methods to solve quadratic equations. I prefer learning this method for all students to know is the best choice than the normal way. Glad how you ended up connecting or even linking to the Quadratic Formula itself.

@mathyou5436 4 жыл бұрын

I really like they way you're emphasising IF -> THEN logic in this video.

@balagopalm5995 4 жыл бұрын

Thank you sir. It's a brilliant way of solving quadratic equations rather than memorising the quadratic formula. Hoping for you to come up with many other tricks to simplify Math

@robertcastillo8157 4 жыл бұрын

This is a great way to approach quadratic equations...great job!

@chinli72 2 жыл бұрын

This method is so much simpler than what I was taught. Bravo Prof. Loh!

@laurachitez8938 4 жыл бұрын

What a wonderful person you are many blessing to you, we need more people like you!

@Josdamale 4 жыл бұрын

A brilliant method brilliantly explained. Much appreciated.

@almightygod1023 4 жыл бұрын

This is amazing. This is" MIRACULOUS " that was very kind of you for sharing this. THANKS A LOT

@harshdeeprandhawa5872 3 жыл бұрын

shoutout to people like this on youtube for carrying us through school single-handedly. THANKYOU

@hyekyungkim6850 3 жыл бұрын

He is the BEST teacher ever! I loved how he teaching way. Thank you!!

@ericofarias254 4 жыл бұрын

Po-Shen Loh's enthusiasm is the best of the video

@laurenbrock5056 2 жыл бұрын

This was amazing! I actually had to pause the video and derive the quadratic formula because I was so excited about noticing how it relates to this method. As soon as I finished I unpaused the video and Professor Loh started talking about how to use the method to derive the quadratic formula. The logical pathway is so satisfying in this video and I am grateful to finally understand the quadratic formula!

@success687 2 жыл бұрын

Hi....

@faruqhsj 4 жыл бұрын

Brilliant way of solving Quads in a more generalistic manner , for helping our natural brain go straight without much of guessing ! You have illustrated so nicely , with great patience in the interests of diverse learners and practitioners , dear friend in Maths ! Bless you ! 👍❤😍✨

@mystiseed9443 3 жыл бұрын

I have just one word for this "AWESOME"

@josenoelteh69 4 жыл бұрын

Unbelievably easy and effective!!! Wish I knew this when I was a lot younger though he he. Thanks heaps. Cheers.

@annakairema6774 3 жыл бұрын

Many thanks for this video! It gave me (and my high school students) new insight into understanding the cubic equation formula which uses the same beautiful ideas explained so well in this video. It never crossed my mind to use these ideas to solve the simpler quadratic equation. So, thank you! Best regards, Anna/Helsinki/Finland

@basalduat 3 жыл бұрын

Thank you Po-Shen!!! You are an extraordinary teacher/lecturer.

@jensimaster 3 жыл бұрын

This is amazing, I am watching your videos to see if they'd be a good resource for my son who's 14, but you just taught a 43 year old engineer something new! Thank you!

@forsadaqah183 4 жыл бұрын

Teachers like you and my best maths teachers(Chandan Sir,Azizul Sir)really inspire the students to discover and love the maths.Much respect to every good and ideal teachers.

@wreckim 2 жыл бұрын

As a 4th grade teacher, I can tell you that it would be incredible to have this kind of talent exposed to the kids right from 1st grade on. So much of the math problems we have is because we lack our natural curiosity and stop having fun. Math gets to be all about 'testing' pretty quick once they leave 6th grade. Thanks for posting, great lesson.

@jenm1 2 жыл бұрын

You could teach them!

@nagzul1 Жыл бұрын

I actually watched the 40:05 minute video without skipping!😂 Just like learning golf, when you can connect with the instructor through the way the knowledge is properly conveyed, then you find gold at the end of the rainbow!🎉😊

@sarahakhtar345 4 жыл бұрын

Few weeks before my gcse exams I find you and I love to your vids I'm defo using these methods in my exams thanks sir. I'm subscribing.

@jacobhouston1655 4 жыл бұрын

I’m going to teach this to all my peers at my community college.

@mathisreallyfun 4 жыл бұрын

Amazing! Will start showing students this too! Thank you!

@psloh 4 жыл бұрын

Nice to connect with a fellow educator!

@mathisreallyfun 4 жыл бұрын

Po-Shen Loh yes! I’m so happy when I saw your video. Really inspiring! Thank you!

@belmer73 4 жыл бұрын

I love the way he teaches, how he anticipates future content, let’s viewers know there is a reason for doing something, his enthusiasm.

@psloh 4 жыл бұрын

Thank you for sharing your thoughts! Math is about reasoning, not about memorizing. Everything in math can be taught in a way which illuminates the reasons. :)

@belmer73 4 жыл бұрын

Po-Shen Loh yes! It’s no good to just memorize. That will be quickly lost. But the ability to explain your way through a concept gives access to so much more.

@psloh 4 жыл бұрын

@@belmer73 :)

@moinmalik1320 4 жыл бұрын

Dr. Loh: The technique of completing the square and its formal form, the quadratic formula, are beautifully re-interpreted to present an easy to handle method. Will always love to tell my students this method, giving your reference (Dr Poh-Shen Loh) and encouraging them to watch on the KZfaq.

@naurnootnoot 3 жыл бұрын

This is groundbreaking material, truly eyeopening

@Futurewarrior507 4 жыл бұрын

Thankyou for giving us, such a nice method to solve the quadratic equations

@esifohawkins4697 Жыл бұрын

I like your teaching style. you actually explained how you arrived at a number which a lot of people don't do. Bravo!!!

@kathygedamke2167 Жыл бұрын

He's actually "completing the square"! Throw the constant on the other side as a negative, take half of b, square that and add it to the number on the other side. Then you take plus or minus the square root, then add the number from the left side. I was actually thinking along those lines a few weeks ago, but didn't have time to follow it through. Hats off to you!

@dlu0813 4 жыл бұрын

Thanks Mr. Loh! You're a great help to my math career and I can't wait to see more challenge videos! :)

@psloh 4 жыл бұрын

Pleasure to share this one with everyone!

@dududaud.4221 4 жыл бұрын

Yes..... He is a genius... Thanks Dr. I love Mathematics my favourite

@academia1798 4 жыл бұрын

Sir your content is highly discussed by Triangular Kamal which is really easy for all kinds of people. kzfaq.info/get/bejne/ebN-d9qKnNebcYk.html

@cakiilunicorn7929 3 жыл бұрын

Can't wait to find this in text books in a few years or so.

@CU96821 4 жыл бұрын

A teacher like you sure would have helped me when I learned math! 😊

@arshhasan2985 3 жыл бұрын

This is the first thing our teacher taught us to use and never waste time!

@JS-yg7fy 3 жыл бұрын

I was taught this, since class 8 in India.

@4theTruthseeker 3 жыл бұрын

Seeing this.. i feel like im recovering from my illness... So unreal.. thank you professor.

@AtunHotepRe 4 жыл бұрын

Much Thanks Prof. Loh ... Outstanding!

@pratyaksh1729 3 жыл бұрын

Its just the quadratic formula

@senthilkr1970 Жыл бұрын

Very interesting and amazingly explained. never imagined i should have seen this 40 min continously without stopping. Great. Love to learn more.

@ramonalejano671 Жыл бұрын

Professor Po-Shen Loh found and original insight. You are amazing!

@shenlongslostballs6443 3 жыл бұрын

It uses the implication of transitive relation 'if' this exists 'and' the next condition Exists 'then' the third condition must exists to satisfy the relation. Thanks a lot sir for this method it's more solid compared to guessing factors

@michaelsienkaah654 Жыл бұрын

You have made me cry

@ly_lols 4 жыл бұрын

This is the most helpful video i've ever seen

@johntaylor181 3 жыл бұрын

The brilliance of this method is only rivalled by the excellence of the presentation! WONDERFUL!!

@pamelafrancis4476 3 жыл бұрын

Thank you for explaining everything so clearly also for your time and trouble in bringing this to everyone.

@ayushmansharma4362 4 жыл бұрын

Thank you very much sir for this wonderful method. I m an indian JEE ASPIRANT and even i m very thankful for this method. I really going to share it with my friends.

@anshumanagrawal346 4 жыл бұрын

But Isn't It Just Completing The Square?

@ayushmansharma4362 4 жыл бұрын

@@anshumanagrawal346 it will come in handy for tricky quartic quadratic equations

@anshumanagrawal346 4 жыл бұрын

@@ayushmansharma4362 oh ok thanks

@guesswho386 4 жыл бұрын

That was absolutely amazing!!!

@jw5287 2 жыл бұрын

love the energy and the great insights, really helped me understand the concept of the formula much better.

@tusharamreliya5250 3 жыл бұрын

Best lecture ever seen on quadratic. Thanks Mr. Loh❤

@maarofyusof1883 4 жыл бұрын

Ok this is fun. Thank you Mr. Loh for detail explanation

@_p0tz_ 4 жыл бұрын

Normal methods require quadratic formulas or completing the square. This method combines the two which makes it easier

@M.Ack11 3 жыл бұрын

Splitting the middle term is also another normal method to solve Q.E

@Amit-cf2lj 4 жыл бұрын

Even student should have a teacher like him.

@huguesl2096 4 жыл бұрын

Thank for this clear and excellent video. I will recommend my students watching your video and use your method.

@trevorallen3212 4 жыл бұрын

Finally I can put factoring aside it's lot more harder guessing than not having to deal with it.

@chocolateangel8743 3 жыл бұрын

This method actually combines factoring with an understanding of palabras (the midpoint, in particular). Once you understand it, I do think it's easier. However, it works better on some problems than others. If there's a leading coefficient other than one and you have to deal with lots of fractions, things get can get messy.

@jjphenom2831 3 жыл бұрын

I am quite surprised that this has not been more widely known. In Germany it is called the pq-Formula (because of x^2+px+q) and it has probably been the most common way it is being taught.

@chocolateangel8743 Жыл бұрын

@JJPhenom I'm American. When I was in school, we were just expected to memorize the Quadratic Formula. It was never explained to us. I had never heard of the PQ Formula -- until I heard of the Po-Shen Loh method and began doing research and watching a lot of videos. I think the way the Po-Shen Loh method is presented (especially when done with a graph) makes it easier to understand & makes the formulas make sense.

@jjphenom2831 Жыл бұрын

@@chocolateangel8743 I absolutely agree. I was only surprised that this is not necessarily the way it has been taught.

@chocolateangel8743 Жыл бұрын

@@jjphenom2831 I think it's because of how generations of math educators have been taught (at least in America). I've talked to a lot, and the idea of learning math on a deeper level, from a more conceptual perspective, is pretty new for us. Back-in-the-day, being good at math just meant that you were good at memorizing algorithms (even if you didn't understand them). Plus, the standards that teachers had to meet in order to teach math were pretty low. When they first raised them, many teachers that had been teaching for years, couldn't pass them. It was a big deal because they also couldn't replace all these teachers. The kids basically got screwed. These teachers were talking about how hard the tests were to pass. So, I asked some professors that had taught at the high school and college levels. They said they weren't that had -- if you understood math. If just tried to get through everything using memorization, you were in trouble.

@jjphenom2831 Жыл бұрын

@@chocolateangel8743 Oh I see. That sounds like an interesting shift in approaches. I will be following up on how successful this turns out to be. Here the formula is often applied quite algorithmically and without going very deep into its derivision. I do not know the reason why this is the predominant method of solving quadratic equatiins though. Would be interesting to see a worldwide distribition

@WoolyCow Жыл бұрын

more people need this in their lives

@sherwoodhikes9709 6 ай бұрын

Thank you very much Prof. Loh for sharing this method. My algebra class will really enjoy this!

@WestalSage 4 жыл бұрын

So in short, it's still the quadratic formula, but force A=1, then simply rewrite sqrt((B^2-4C))/2 as sqrt( (B/2)^2 - C ) I agree that this makes it simpler, and I think the key is that you're dealing with B/2 on both sides of the plus/minus.

@_This_is_L_ 4 жыл бұрын

Nice meeting again! I think this vdo clears the doubt we were having with that method....

@vishnukumarsingh4966 2 жыл бұрын

This is Shridhar Acharya formula which is already there in class 9 textbooks.

@tuonglannguyen4012 4 жыл бұрын

Thanks professor for very meaningful video, really love the way you express the logic and guide how to produce the result, actually in real use it will be very quick by just writing down neccesary part to calculate. And in fact i learnt 1 new trick of solving sys of equations consists of a product & a sum (the average plus/minus). Also i would like to contribute another approach for this as well: x^2 + bx + c = [x^2 + (2b/2)x + 1/4] + c - 1/4 = (x + 1/2)^2 + c - 1/4 . It's look a bit complicated but if understand how to express (a + b)^2 should be very easy to imagine. But then, just another trick, and the important is still how we understand things and utilize them the right way.

@johnmellor6065 4 жыл бұрын

brilliant explanation you have took the guessing out of the equation thanks

@ravikrpranavam 4 жыл бұрын

Thank you, I loved your method, it is easier to get the solutions!

@capheny368 4 жыл бұрын

I was just curious about the name of this method. shall we call it the Po-Shen law as the title of your name professor

@psloh 4 жыл бұрын

You're welcome to call it whatever you wish! To help people quickly identify the method, you are welcome to mention my name because then the Internet searches will quickly turn it up. :)

@rukmaniranganathan8420 4 жыл бұрын

Super name

@cursebr2937 4 жыл бұрын

Nope

@ehsaanulhaque1857 4 жыл бұрын

Po-Shen Loh fake.

@creativeclub2023 4 жыл бұрын

@leobitoff8792 4 жыл бұрын

Ez, also useful in solving extraneous solutions among irrational equations and inequalities

@rekhaparmar9259 3 жыл бұрын

The first time I had my own way started to studying because of you

@july4cat 3 жыл бұрын

I'm a little surprised that this is considered a novel thing in the US. I learned this as the "standard" method for solving quadratic equations in junior high in China. But Prof. Loh still kept me engaged. Great professor!

@perpetuallyconfused2508 3 жыл бұрын

we did this thing called the quadratic formula that enabled us to solve any quadratic equation in Hong Kong. if i remember correctly, it was (-b+/-(b^2-4ac)^1/2)/2a if u do manage to remember it, solving quadratic equations is quite simple as well