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Q.

The cubic polynomial with the sum of the roots, sum of the product of its zeroes taken two at a time and product of its zeroes are $2, - 7, - 14$ respectively is

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a

x^{3} - 2 x^{2} - 7 x - 14

b

x^{3} + 2 x^{2} + 7 x + 14

c

x^{2} - 2 x^{2} - 7 x + 14

d

x^{3} - 2 x^{2} + 7 x - 14

answer is C.

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Detailed Solution

α + β + γ = 2

$α β + β γ + α γ = - 7$

$α β γ = - 14$

Cubic polynomial is $x^{3} - (α + β + γ) x^{2} + (α β + β γ + γ α) x - α β γ$

$= x^{2} - 2 x^{2} - 7 x + 14$

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The cubic polynomial with the sum of the roots, sum of the product of its zeroes taken two at a time and product of its zeroes are 2,−7,−14 respectively is