Question

Given that one of the zeroes of the cubic polynomial $a{x}^3+b{x}^2+cx+d$ is zero, the product of the other two zeroes is

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

Answer 1

The correct option is B

$\frac{c}{a}$

Let $\alpha ,\beta$ and $\gamma$ are the roots of given cubic polynomial

Since one of the zeroes is zero.

Let say $\gamma =0$

Sum of the zeroes = $-\frac{b}{a}$

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

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

Products of zeroes taken two at a time = $\frac{c}{a}$

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

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