What is the value of $k$ for which the HCF of $2 x^{2} + k x - 12$ and $x^{2} + x - 2 k - 2$ is $(x + 4)$ ?

5

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7

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10

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- 4

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Solution

The correct option is A $5$
$(x + 4)$ is HCF $\Rightarrow x = - 4$ is As solution
of $2 x^{2} + k x - 12 & x^{2} + x - 2 x - 2$
$\Rightarrow 2 (- 4)^{2} + k (- 4) - 12 = 0 \Rightarrow k = 5$
$\Rightarrow (- 4)^{2} - 4 - 2 k - 2 = 0 \Rightarrow k = 5$

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