If 0 is one zero of the polynomial $a x 3 + b x 2 + c x + d,$ then what will be the product of the other two zeroes?

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− c a

c a

b a

− b a

answer is B.

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Detailed Solution

Given that one of the three zeroes of the polynomial

a x 3 + b x 2 + c x + d

is 0.
If

α, β, and γ

are the zeroes of the cubic polynomial

a x 3 + b x 2 + c x + d,

then

α + β + γ = − b a α β + β γ + γ α = c a (1) and α β γ = − d a

Given that one of the three zeroes is 0.
Let

α = 0.

Substitute

α = 0

in equation (1), we get,

α β + β γ + γ α = c a

⇒ (0) β + β γ + γ (0) = c a

⇒ β γ = c a

So the product of the other two zeroes is

c a .

Hence option (2) is correct.

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