Question

Given that one of the zeroes of the cubic polynomial ${\mathrm{ax}}^3+{\mathrm{bx}}^2+\mathrm{cx}+\mathrm{d}$ is $0$. The product of other two roots is:

• A. $\frac{-\mathrm{c}}{\mathrm{a}}$
• B. $\frac{\mathrm{c}}{\mathrm{a}}$
• C. $0$
• D. $\frac{-\mathrm{b}}{\mathrm{a}}$

Answer 1

The correct option is B

$\frac{\mathrm{c}}{\mathrm{a}}$

Explanation for the correct options:

Using the property of the roots of a cubic polynomial:

Let $\alpha ,\mathrm{\beta },\mathrm{\gamma }$be the three roots of the cubic polynomial and $\alpha =0$.

$\mathrm{\alpha \beta }+\mathrm{\beta \gamma }+\mathrm{\gamma \alpha }=\frac{\mathrm{c}}{\mathrm{a}}$

and $\alpha =0$ (Given)

$\Rightarrow 0+\mathrm{\beta \gamma }+0=\frac{\mathrm{c}}{\mathrm{a}}$

$\mathrm{\beta },\mathrm{\gamma }$ were the other two roots and their product came out to be $\frac{\mathrm{c}}{\mathrm{a}}$.

Hence, option (B) is the correct answer.