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

Given:

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

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

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,

$f(-a)=0$

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

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

$\Rightarrow 3a+4=0$

$\Rightarrow 3a=-4$

$\Rightarrow a=\frac{-4}{3}$

The value of $a$ is $\frac{-4}{3}$.    

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Updated on: 10-Oct-2022

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