Question

Question 5
Given that one of the zeroes of the cubic polynomial ax 3 + bx2 + 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

Let p (x)= $a{x}^3+bx2+cx+d$
Given that, one of the zeroes of the cubic polynomial p(x) is zero.
We know that,
Sum of product of two zeroes at a time = $\frac{c}{a}$
$\Rightarrow \alpha \beta +\beta y+y\alpha =\frac{c}{a}$
$\Rightarrow 0\times \beta y+y\times 0=\frac{c}{a}$
$\Rightarrow 0+\beta y+0=\frac{c}{a}$
$\Rightarrow \beta y=\frac{c}{a}$
Hence, product of other two zeroes = $\frac{c}{a}$