If the expression $5 x^{2} + 9 x y + c y^{2}$ can be resolved into product of two linear factors, then $c$ takes the value :

- 2

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2

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- 3

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3

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Solution

The correct option is A $- 2$
$5 x^{2} + 9 x y + c y^{2}$
for $c = - 2$
$= 5 x^{2} + 9 x y - 2 y^{2}$
$= 5 x^{2} + 10 x y - x y - 2 y^{2}$
$= 5 x (x + 2 y) - y (x + 2 y)$
$(5 x - y) (x + 2 y)$

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