If $α & β$ are the zeroes of a quadratic polynomial p(x), and k is any constant, then what is the general form of the polynomial?

k [x^{2} - (α + β) x + α β]

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k x^{2} - (α + β) x - α β

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k x^{2} + (α + β) x - α β

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k^{2} x^{2} + k (α + β) x + k α β

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Solution

The correct option is A $k [x^{2} - (α + β) x + α β]$
Given, $α & β$ are the zeroes of the quadratic polynomial p(x).

This polynomial should be equal to zero when $x = α$ or $x = β$ .

$\Rightarrow x - α, x - β$ are factors of p(x).

$\Rightarrow p (x) = k (x - α) (x - β)$

$\Rightarrow p (x) = k [x^{2} - (α + β) x + α β]$

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