If one of the zeros of the cubic polynomial
Question:

If one of the zeros of the cubic polynomial $a x^{3}+b \times 2+c x+d$ is 0 , then the product of the other two zeros is

(a) $\frac{-c}{a}$

(b) $\frac{c}{a}$

(c) 0

(d) $\frac{-b}{a}$

Solution:

(b) $\frac{c}{a}$

Let $\alpha, \beta$ and 0 be the zeroes of $a x^{3}+b x^{2}+c x+d$.

Then, sum of the products of zeroes taking two at at a time is given by

$(\alpha \beta+\beta \times 0+\alpha \times 0)=\frac{c}{a}$

$=>\alpha \beta=\frac{c}{a}$

$\therefore$ The product of the other two zeroes is $\frac{c}{a}$.