so you want to see the cubic formula

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0:00 we will derive the cubic formula
0:07 review on solving the quadratic equation x^2+px+q=0 and the pq-formula
6:17 part1, get rid of the x^2 term in the y-world (let x=y-b/(3a))
17:23 part 2, solving y^3+py+q=0 (let y=z-p/(3z))
39:27 part 3, put everything together
#maths #imaginarynumber #blackpenredpen

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Here’s a similar formula for quintic. de Moivre quintic formula

blackpenredpen

Finally, a handy formula I can use when I come across x^3 + 3x^2 + 3x + 1 = 0

edwardhuang

I don't speak English much but this guy explains it so simply and in such detail that I understand everything. Very interesting.

alexeton

Finally a real derivation of the cubic formula. It's honestly not terribly difficult to follow, just tedious.

hppjsyk

Tip:
In ax³+bx²+cx+d=0
Before going to the formula try this.
If a+b+c+d=0, x=1
If (a+c)-(b+d)=0, x= -1

Afterwards you can factor it into a quadratic easily.

Ex.
2x³+5x²+2x-1=0
Test1: 2+5+2-1=0 ---> false. x≠1
Test2: (2+2)-(5-1)=0
4-4=0 ---> true. x= -1

Now factor: with solution (x=-1)
2-0=2, -1×2= -2, 5-2=3, -1×3=-3, 2-3=-1, (-1)×(-1)=1, -1+1=0. Getting 0 means x=-1 is valid solution.(if not then its incorrect solution)
Now take all numbers from the addition and subtraction results in order.
2, 3, -1, 0 and now you get a quadratic.
2x²+3x-1=0
x²+3/2x=1/2
x²+3/2x+9/16=1/2+9/16
(x+3/4)²=17/16
x=-3/4+-sqrt17/4.

X[1, 2, 3]={-1, (-3-sqrt17)/4, (sqrt17-3)/4}

Awesome-ctvr

I love learning derivations for things;
it feels a lot better to have the skill to derive as many formulas as possible, instead of having to look them up in tables.

Peter_

This was a blast to watch. I watched the whole thing while not feeling bored, because the process was just so adventurous and fun. Can’t believe the dedication put into the presentation of this formula

Wmann

I love how you finally talked about the p-q-formular. In germany we students only learn this formular to solve quadratic equations. We were never taught abc-formular. It always confused me why every youtuber uses a different formular. I thought the p-q-formular would never be used somewhere else in the world because of that.😅

Jonny_XD_

I tried deriving it myself but I got stuck at the complex analysis part so thank you for explaining it. it makes more sense now 😊

tzkitud

You can use a rhyme to remember the quadratic formula. This needs a whole song though 😵

fantiscious

Finally a great masterpiece, was very curious about this cubic formula...

sriprasadjoshi

Hey BPRP, I just wanted to thank you for posting this video. I know this was a ton of work and took a lot of planning, and I really appreciate the effort you put into here. It definitely did not go unnoticed over here. You’ve been one of my favorite math educators ever sense I discovered your channel. I have been subscribed for almost a year now and in that time you have taught me so much. Even more, I have been trying to solve the Cubic formula for a couple months, and had recently given up thinking it was too hard and you come up and post a clear proof explaining how and why each step works. You have inspired me to think critically about problems and also kindled in me a love for math that will affect me in my college studies coming up. You are the best. Keep up the great work!

maxwelljohnson

7:15 'and this is then actually just a quadratic formula in terms of z^3'
Thanks to watching you for years, I am actually able to follow ❤

haaansolo

i had so much fun watching this video!! all this time ive been wondering how people get the cubic equation. i'm in 7th grade and i have just been a math fanatic since june 2022 and i have improved a lot since then. it got to the point that i understand calculus and how to do those limits, l'h rule, that type of thing. basically what im trying to say is i enjoyed this video a lot and it felt like i dived into the math rabbithole.

howdoi_yt

Now WE need a video for the quartic formula

ThetaMaths

Je suis un prof de math et j'adore votre méthode par laquelle vous expliquez des concepts mathématiques. Bravo ❤

ramzidaous

I love the energy you have while teaching, you really do like what you are doing thats cool

boltez

due to some complicated equation formula, my attention was diverted to the first 100 or 200 numbers of e and the stacks of markers at the back. (but this is very useful, thx for this video…it helped me alot)

lemondrop

Pls give this man an infinitely large board so that he dont need to rub every time 😭😭 great explanation sir

omkartikekar

Fantastic! I was wondering how the cubic formula can be derived. Thanks for explaining!

jakobthomsen

so you want to see the cubic formula

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