Question

Roots of 3rd degree equation sum of roots

Answer 1

let the polynomial be ax³+bx²+cx+d = 0
whose roots are α,β,γ
 then,
x3+(b/a)x²+(c/a)x+(d/a) = (x-α)(x-β)(x-γ)
= x3 - (∑α)x² + (∑αβ)x - αβγ

sum = -b/a 

Answer 2

A polynomial of 3 rd degree equation can be written as :

$\boxed{a x^3 + b x^2 + c x + d = 0}$

Lets say p,q and r are the roots of the equation..................

$\mathfrak{\underlined{Sum\:of\:roots}}$

$p + q + r =\boxed{-\frac{b}{a}}$

$\math\frak{\underlined{Product\:of\:roots}}$

$p q r =\boxed{-\frac{d}{a}}$

Also remember that:

$pq + pr + qr = \boxed{\frac{c}{a}}$

Hope it helps you

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