If (x+a) is a factor of 2 x^2+2 a x+5 x+10, find a. - Vidyadip

Question

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

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Answer

$x+a$ is a factor of
$f(x)=2 x^2+2 a x+5 x+10$
Let $x+a=0, x=-a$
$\therefore f(-a)=2(-a)^2+2 a(-a)+5(-a)+10$
$=2 a^2-2 a^2-5 a+10=-5 a+10$
$\because x + a$ is its factor
$\therefore f(-a)=0$
$\Rightarrow-5 a+10=0 \Rightarrow 5 a=10 \Rightarrow a=2$
Hence $a=2$

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Very-Short-Answer Question:
If $(x + a)$ is a factor of $(2x^2 + 2ax + 5x + 10)$, find the value of a.