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If $(x + 2)$ is the G.C.D of the polynomials $(x - 4) (2 x^{2} + x - a)$ and $(x + 1) (2 x^{2} + b x - 12)$ , then the value of $(5 a - 6 b)$ is

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$- 42$

$42$

$24$

$- 24$

answer is B.

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Detailed Solution

$(x + 2)$ is G.C.D of $f (x)$ and $g (x) \Rightarrow f (- 2) = 0; g (- 2) = 0 \Rightarrow f (- 2) = 8 - 2 - a = 0 \Rightarrow a = 6$

$g (- 2) = 2 b = - 4 \Rightarrow b = - 2$

$\Rightarrow 5 a - 6 b = 5 (6) - 6 (- 2) = 42$

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