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Given that one of the zeroes of the cubic polynomial $a x 3 + b x 2 + c x + d$ is zero, then what is the product of the other two zeroes?

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− c a

c a

0

− b a

answer is B.

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Detailed Solution

Given

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

.
Since 0 is the zero of polynomial, then

a (0) 3 + b (0) 2 + c (0) + d = 0 d = 0

Now, substitute

d = 0

in the given polynomial, and we have

a x 3 + b x 2 + c x + 0 = 0 a x 3 + b x 2 + c x = 0 x (a x 2 + b x + c) = 0 a x 2 + b x + c = 0

The product of the obtained quadratic equation is equal to the ratio of the constant term and the coefficient of

x 2

, (i.e.)

c a

.
Hence, the correct option is 2.

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