If (x-p) and (x-q) are the factors of the expression $a x^{2} + b x + c$ , then the values of $a$ and $b$ are:

-1, -(p + q)

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1, p + q

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1, -(p+q)

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None of these

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Solution

The correct option is C
1, -(p+q)

(x-p) and (x-q) are the factors of the expression $a x^{2} + b x + c$ ,

$\Rightarrow$ $a x^{2} + b x + c = (x - p) (x - q)$

$⟹ a x^{2} + b x + c = x^{2} - (p + q) x + p q$

By comparing the co-efficients of $x^{2}$ , $x$ and the constant term,we get,

$a = 1$ , $b = - (p + q)$ and $c = p q$

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