If $(x + a)$ is a factor of $2 x^{2} + 2 a x + 5 x + 10,$ find $a$ .

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Solution

Given $f (x)$ $= 2 x^{2} + 2 a x + 5 x + 10$

$g (x) = x + a$

$x + a = 0$

$x = - a$

$f (- a) = 2 (- a)^{2} + 2 a (- a) + 5 (- a) + 10$

$\Rightarrow + 2 a^{2} - 2 a^{2} - 5 a + 10 = 0$

$\Rightarrow 5 a = 10$

$\Rightarrow a = \frac{10}{5}$

$∴ a = 2$

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