Find a cubic polynomial having sum of zeroes, sum of product of its zeroes taken two at a time and product of its zeroes as 5,-3 and -7 respectively.

k (x^{3} - 5 x^{2} + 3 x + 7)

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k (x^{3} + 5 x^{2} - 3 x + 7)

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k (x^{3} - 5 x^{2} - 3 x + 7)

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k (x^{3} - 5 x^{2} - 3 x - 7)

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Solution

The correct option is C

$k (x^{3} - 5 x^{2} - 3 x + 7)$
$L e t α, β, γ are the zeroes of the given polynomial. S = α + β + γ = 5 S_{p} = α β + β γ + γ α = - 3 P = α β γ = - 7 Required cubic polynomial is = k [x^{3} - S x^{2} + S_{p} x - P] = k [x^{3} - 5 x^{2} + (- 3) x - (- 7)] = k [x^{3} - 5 x^{2} - 3 x + 7]$
So, the correct option is c.

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