# Thread: Understanding how the proof introduced a new coeffecient

1. ## Understanding the proof of quartic formula

Hello. I have some difficulties understanding a proof of solving quartic equation by using quartic formula. On page 2 of the proof, the author had introduced a new coefficient. Is there substitution from any line? What is the substitution? Thank you for your help.

2. ## Re: Understanding the proof of quartic formula

Originally Posted by Cbarker1
Hello. I have some difficulties understanding a proof of solving quartic equation by using quartic formula. On page 2 of the proof, the author had introduced a new coefficient. What is the substitution to a previous line. Thank you for your help.
Do not post questions as attachments.
Are you so lazy as to not be able to type out the question?
Also you you can use LaTeX code on this site.
If you really want help, do one of those two options.

3. ## Re: Understanding how the proof introduced a new coeffecient

No. I am not lazy, but why are you attacking me. I have hard time use LaTex. The writing whole proof will be a boondoggle of time.

4. ## Re: Understanding how the proof introduced a new coeffecient

Originally Posted by Cbarker1
No. I am not lazy, but why are you attacking me. I have hard time use LaTex. The writing whole proof will be a boondoggle of time.
Type your question. It cannot be that hard. Otherwise you are lazy.

5. ## Re: Understanding how the proof introduced a new coeffecient

i will give the website, then. will it be fine then?

7. ## Re: Understanding how the proof introduced a new coeffecient

There's no need for anyone to get upset. The point Plato is making is that most members here do not like to download unknown files to their computer, because there is the risk of downloading viruses. On the other hand, the OP has stated that this is a long proof, and typing it out is long and tedious, especially not being familiar with LaTeX.

On the subject of the original question, which is the "new coefficient" you do not understand?

8. ## Re: Understanding how the proof introduced a new coeffecient

where the (Sy+T)^2; what is S stand for?

9. ## Re: Understanding how the proof introduced a new coeffecient

I believe you need to read the "Solving Cubics" PDF in order to understand what is happening in that step.

Edit: No you don't. What it is saying is that with the lines talking about solving for z, all it's saying is that in order for the RHS of your equation involving y to be a perfect square, then the discriminant must be 0, which in turn creates a cubic equation in z. Since all cubics have at least one solution, then there is definitely a value of z which satisfies the RHS of your equation involving y being turned into a perfect square. Therefore, it is reasonable that you can write the RHS as (Sy + T)^2, where S and T are some constants.