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A cubic polynomial with the sum of zeros, the sum of the product of its zeroes taken two at a time, and the product of its zeroes as 2, –7, –14 respectively. The cubic polynomial is:

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x 3 + 2 x 2 − 7 x + 10

x 3 + 2 x 2 − 7 x + 14

x 3 + 2 x 2 − 7 x + 5

x 3 + 2 x 2 − 7 x + 6

answer is B.

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Detailed Solution

Given that the sum of zeros, the sum of the product of its zeroes taken two at a time, and the product of its zeroes are 2, –7 and –14.
Assume

α, β and γ

are 3 zeros of the cubic polynomial,

α + β + γ

= -2
But we know that,

α + β + γ

− b a

− b a = − 2 b a = 2

b a = 21

Also,

α β + β γ + γ α

= -7
But we know that,

α β + β γ + γ α = c a

c a = − 7

c a = − 7 1

Also,

α β γ

= − 14

But we know that,

α β γ

− d a

− d a = − 14

d a = 14

b a = 21 c a = − 7 1 d a = 141

Now, after comparing and simplifying the value are
a = 1, b = 2, c = -7 and d = 14.
The general form of cubic polynomial is,

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

The polynomial is,

x 3 + 2 x 2 − 7 x + 14

Hence, option 2 is correct.

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