In each of the following, two polynomials, find the value of $a$, if $x + a$ is a factor.$x^4 - a^2x^2 + 3x - a$

Given:

Given expression is $x^4 - a^2x^2 + 3x - a$.

$x + a$ is a factor of $x^4 - a^2x^2 + 3x - a$.

To do:

We have to find the value of $a$.

Solution:

We know that,

If $(x-m)$ is a root of $f(x)$ then $f(m)=0$.

Therefore,

$f(-a)=0$

$\Rightarrow (-a)^4-a^2(-a)^2 + 3(-a) - a=0$

$\Rightarrow a^4-a^4-3a-a=0$

$\Rightarrow -4a=0$

$\Rightarrow a=0$

The value of $a$ is $0$.     

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Updated on: 10-Oct-2022

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