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If $x^{2} + x - 2$ is G.C.D of the expressions $(x - 1) (2 x^{2} + a x + 2)$ and $(x + 2) (3 x^{2} + b x + 1),$ then the values of a and b respectively are

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- 5, - 4

5, - 4

- 5, 4

4, 5

answer is B.

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Detailed Solution

G . C . D

= x^{2} + x - 2 = (x - 1) (x + 2)

$f (x) = (x - 1) (2 x^{2} + a x + 2)$

$g (x) = (x + 2) (3 x^{2} + b x + 1)$

$x - 1$ is a factors of $3 x^{2} + b x + 1 \Rightarrow b = - 4$

$x + 2$ is a factor of $2 x^{2} + a x + 2 \Rightarrow a = 5$

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