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

Question

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

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Answer

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

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