Cubic Formula Proof

Derivation by Rawiri Mahue. Software and style inspired by Khan Academy.

[mahmoudalbahar]

I really thank you for this cubic formula past I downloaded this proof in computer I watched it and I were solving with you it takes nearly 5.5

[lucasvo]

he went from (a+b)^2=a^2+2ab+b^2

to e^i theta = cos(theta)+i sin(theta)

[HDitzzDH]

Whoever originally came up with all of these substitutions for the cubic formula must have been on something..

[AzianaTeh]

Thank for this detailed tutorial. This is important for my research estimated regression line to approximate week and moisture content of the oil palm. Since quartic polynomial includes to determine the cubic polynomial real root as well.

[riyan]

The scariest moment was when he started drawing complex plane

[nathanezra]

Why do u make all of these substitutions? How do we know it will simply the expression at hand?

[lmmgt]

I recommend student read about the " depressed equation". a very very interesting story.

[maximusmeridius]

How did you think of the substitution x = y - b/3a ?

[carlosdecabodelavega]

Minute 3: I get it
Minute 52: It´s chinese to me.

[suvenduseth]

How do we know that we have to make the specific substitution of the value of x

[reubenmanzo]

Why is s important? Why can't we just substitute y=z-e/3z?

[king_noah]

15:50 I don't understand
17:34
26:07
33:44
36:00
Wait isn't Euler's identity for the constant e? I'm so confused how he can use that for the variable too! 38:28
I just realized. What did he do with the "i" terms in the steps shown on screen at 46:12 ? Never mind, just realized that he only used on value of z so far.
46:31 What did he just do here? I'm really confused. 47:15 Never mind. He just used the "y = z - e/(3z)" substitution.
48:29 I don't know how to verify that for myself, but okay!

[nathanezra]

How did we know that we were supposed to substitute y - 3/a for x.

[davedonnie]

So when you put e in the substitution the first time, did you mean some variable e or euler's number?

[atlast]

It's an outstanding video, excellent job! But you tend to make a sort of wet champing like noise with your tongue, and once you pick up on it it can be quite annoying.

[overlordprincekhan]

But why did you substitute? Give the proof of this!

[holyshit]

I prefer y = u+v substitution which gives us Vieta formulas for quadratic
because we dont need to take care of root equal to zero which will give division by zero

[infoforyou]

genius bro but i want reply of my comment, basically i just want to know can we also derive the formula of nth degree polynomial.

[bowlineobama]

What a mess. Too many substitutions of variables confused me. I would like to see how you apply these three equations in a real cubic equation, where you have constants a, b, c and d are given.

[siragan]

I wish you use a different colour board!!! instead of Black