Thread: cubic equation proof needed

Say the equation is

ax3+bx2+cx+d=0

suppose that he roots of this equation are α,β, and γ.
How to prove that,
1) α+β+γ = -b/a
2) αβγ=d/a

Originally Posted by callkalpa

Say the equation is

ax3+bx2+cx+d=0

suppose that he roots of this equation are α,β, and γ.
How to prove that,
1) α+β+γ = -b/a
2) αβγ=d/a

Start by reading this: Vieta's Formulas -- from Wolfram MathWorld

Then use Google.

Hello, callkalpa!

Say the equation is: .

Suppose that the roots of this equation are: .

Prove that:

. .
. .

Divide the equation by .[1]


Since are roots, the equation has the form:
. .

which simplifies to:
. . .[2]


Equate coefficients of [1] and [2]:

. .


Therefore: .