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Relationship Between Zeroes and Coefficients of a Quadratic Polynomial

If α&β are th...

Question

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 (x^{2} - (α + β) x + α β)

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Solution

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

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

Thus, p(x) = $k (x - α) (x - β)$

$= k x^{2} - (α + β) x + α β$

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