MCQ
If x + a is a factor of $x^4-a^2 x^2+3 x-6 a$, then a is:
- ✓$0$
- B$-1$
- C$1$
- D$2$
✓
Answer
Correct option: A.
$0$
$x+a$ is a factor of polynomial $f(x)=x^4-a^2 x^2+3 x-6 a$,
$\text { Then at } x=-a, p(x)=0$
$\Rightarrow(-a)^4-a^2(-a)^2+3(-a)-6 a=0$
$\Rightarrow a^4-a^4-3 a-6 a=0$
$\Rightarrow-9 a=0$
$\Rightarrow a=0$
$\text { Then at } x=-a, p(x)=0$
$\Rightarrow(-a)^4-a^2(-a)^2+3(-a)-6 a=0$
$\Rightarrow a^4-a^4-3 a-6 a=0$
$\Rightarrow-9 a=0$
$\Rightarrow a=0$
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