‘-p’ and ‘q’ are the zeroes of the polynomial
$x^{2} - b x + c$ .
The zeroes of the polynomial $x^{2} - b x y + c y^{2}$ are

-py,qy

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py,-qy

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py,qy

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None of these

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Solution

The correct option is A
-py,qy

‘-p’ and ‘q’ are the zeroes of the polynomial $x^{2} - b x + c$ .
$⟹ x^{2} - b x + c = (x + p) (x - q)$ .
$⟹ x^{2} - b x + c = x^{2} + p x - q x - p q$
$⟹ - b = p - q, and c = - p q$
$x^{2} - b x y + c y^{2} = x^{2} - (p - q) x y - p q y^{2}$
$= x^{2} - (p y - q y) x - (p y) (q y)$
$= (x + p y) (x - q y)$

Thus, the zeroes of the polynomial $x^{2} - b x y + c y^{2}$ are $- p y$ and $q y$ .

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