Question

If two of the zeros of the cubic polynomial $ax^{3}+bx^{2}+cx+d$ are each equal to zero, then the third zero is
(a) $\frac{-d}{a}$
(b) $\frac{c}{a}$
(c) $\frac{-b}{a}$
(d) $\frac{b}{a}$

Answer 1

SOLUTION :

The correct option is (c) : - b/a.

Let α, β, γ are the three Zeroes of the cubic  polynomial and α =  β = 0

Given :  The cubic  polynomial f(x) = ax³ + bx² + cx + d  

Sum of zeroes of cubic  polynomial= −coefficient of x² / coefficient of x³

α + β + γ = −b/a

0 + 0 +  γ = −b/a

γ = −b/a

Hence, the third zero (γ) is −b/a .

HOPE THIS ANSWER WILL HELP YOU..

Answer 2

as we know sum of zeroes = ( - coefficient of x^2)/coefficient of x^3

As two zeroes are 0

so third zero = -b/a