Question

Given that two of the zeroes of the cubic polynomial $a{x}^3+b{x}^2+cx+d$are $0$, then find the third zero?

Answer 1

Find the third zero using the other two zeroes:

For polynomial $a{x}^3+b{x}^2+cx+d$, the zeroes are $\alpha ,\beta ,\gamma$.

We know that the Sum of the zeroes of a cubic polynomial is $\frac{-b}{a}$.

Given that the two zeroes are $0$

$\therefore$ $\alpha =0,\beta =0$

Now,

$\alpha +\beta +\gamma =\frac{-b}{a}$

$$\begin{gathered} 0+0+\gamma =\frac{-b}{a} \\ \gamma =\frac{-b}{a} \end{gathered}$$

Therefore, the third zero of the polynomial $a{x}^3+b{x}^2+cx+d$ is $\frac{-b}{a}$.