Question
If $x + a$ is a factor of $x^4 - a^2x^2 + 3x - 6a,$ then $a =$
✓
Answer
Put $x + a = 0 \Rightarrow x = -a$
Then, value of $x^4 - a^2x^2 + 3x - 6a$ at $x = -a$ is zero
Therefore, $(-a)^4 - a^2(-a)^2 + 3(-a) - 6a = 0$
$-9a = 0 \Rightarrow a = 0$
Then, value of $x^4 - a^2x^2 + 3x - 6a$ at $x = -a$ is zero
Therefore, $(-a)^4 - a^2(-a)^2 + 3(-a) - 6a = 0$
$-9a = 0 \Rightarrow a = 0$
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