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If $f (x) = alog x + b x^{2} + x$ has extreme values at $x = - 1, x = 2$ then $a$ = ......., $b$ = .........

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$2, \frac{- 1}{2}$

$\frac{- 1}{2}, 2$

$\frac{1}{2}, 2$

$2, \frac{1}{2}$

answer is A.

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Detailed Solution

$f^{1} (- 1) = 0 \Rightarrow - a - 2 b + 1 = 0$

$\Rightarrow f^{1} (2) = 0 \Rightarrow \frac{a}{2} + 4 b + 1 = 0$

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