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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.

The polynomial must be equal to zero when

$x = α$ and $x = β$

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

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

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