Question

Two of the zeroes of the cubic polynomial $a{x}^3+b{x}^2+cx+d$ is 0, find the third zero.

Answer 1

Let the roots be $p,q,r$.

Given that,

Two roots let $p$ and $q$ be $0$

We know that,

Sum of roots $=\frac{-b}{a}$

$\begin{array}{c}\Rightarrow p+q+r=\frac{-b}{a}\\ \Rightarrow 0+0+r=\frac{-b}{a}\\ \Rightarrow r=-\left(\frac{b}{a}\right)\end{array}$

$\therefore$ Third zero is -b/a