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

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

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

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

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

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Solution

The correct option is A $k (x^{3} - 2 x^{2} - 7 x + 14)$
Let, $α, β, γ$ be the zeros of the given cubic polynomial. Then, we have
$α + β + γ = 2$
$α β + β γ + γ α = - 7$
$α β γ = - 14$
Now, the required polynomial $= k \times [x^{3} - (α + β + γ) x^{2} + (α β + β γ + γ α) x - (α β γ)]$ , where k is real constant.
$= k \times [x^{3} - 2 x^{2} + (- 7) x - (- 14)]$
$= k \times (x^{3} - 2 x^{2} - 7 x + 14)$

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