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If p and q are the roots of the quadratic equation $a x^{2} + b x + c = 0$ then $\lim_{x \to p} {(1 + a x^{2} + b x + c)}^{\frac{1}{x - p}} =$

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$a (p - q)$

$\log [a (p - q)]$

$e^{a (p - q)}$

$e^{a (q - p)}$

answer is C.

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Detailed Solution

$\lim_{x \to p} {[1 + a (x - p) (x - q)]}^{\frac{1}{a (x - p) (x - q)}}^{\times a (x - q)} = e^{a (p - q)}$

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