If (x + a) is a factor of


If $(x+a)$ is a factor of $\left(2 x^{2}+2 a x+5 x+10\right)$, find the value of $a .$



Given: (x + a) is a factor of 2x2 + 2ax + 5x + 10
We have


$\Rightarrow x=-a$

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

Hence, It will satisfy the above polynomial

$\therefore 2(-a)^{2}+2 a(-a)+5(-a)+10=0$

$\Rightarrow-5 a+10=0$

$\Rightarrow a=2$

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