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

Answer 1

The correct option is B $\frac{c}{a}$

According to the question,
We have the polynomial,
$a{x}^3+b{x}^2+cx+d$
We know that,
Sum of product of roots of a cubic equation is given by $\frac{c}{a}$

It is given that one root = 0
Now, let the other roots be α, β
So, we get,
αβ + β(0) + (0)α = $\frac{c}{a}$
αβ = $\frac{c}{a}$
Hence, the product of other two roots is $\frac{c}{a}$