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Find a cubic polynomial with the sum of its zeroes, sum of the product of its zeroes taken two at a time and product of its zeroes as 2, -7, - 14 respectively.

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k (x^{3} - 7 x^{2} - 2 x + 14)

k (x^{3} - 2 x^{2} - 7 x + 14)

k (x^{3} - 7 x^{2} - 7 x + 14)

k (x^{3} - 2 x^{2} + 7 x + 14)

answer is A.

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Detailed Solution

Given, the sum of its zeroes, sum of the product of its zeroes taken two at a time and product of its zeroes as 2, -7, - 14 respectively.
We need to find the cubic polynomial.
Let us assume

α, β, γ

be the zeroes of the given cubic polynomial.
Then, substituting and solving,

α + β + γ = 2

αβ + βγ + γα = - 7

αβγ = - 14

Now, the required polynomial will be,

k \times [x^{3} - (α + β + γ) x^{2} + (αβ + βγ + γα) x - (αβγ)],

where k is real constant.

\Rightarrow k \times [x^{3} - 2 x^{2} + (- 7) x - (- 14)

\Rightarrow k (x^{3} - 2 x^{2} - 7 x + 14)

Therefore, the required cubic polynomial is

k (x^{3} - 2 x^{2} - 7 x + 14) .

Hence, the correct option is 1.

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