Question

Given that one of the zeroes of the cubic polynomial ax3 + bx2 + cx + d is zero, the
product of the other two zeroes is

Answer 1

Answer:

$\frac{c}{a}$

Step-by-step explanation:

We know that in a cubic polynomial,

Sum of zeroes taken two at a time = $\frac{Coefficient of x}{Coefficient of x^3}$

⇒ αβ + βγ + γα = $\frac{c}{a}$, where α, β, γ are the zeroes of the cubic polynomial.

But it is given that one of the zeroes is 0. Let γ = 0.

⇒ αβ + β(0) + (0)α = $\frac{c}{a}$

⇒ αβ = $\frac{c}{a}$, which is the product of the other two zeroes.