In each of the following two polynomials, find the values of $a$, if $x - a$ is a factor:$x^6 - ax^5 + x^4-ax^3 + 3x-a + 2$

Given:

Given expression is $x^6 - ax^5 + x^4-ax^3 + 3x-a + 2$.

$x - a$ is a factor of $x^6 - ax^5 + x^4-ax^3 + 3x-a + 2$.

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,

$f(a)=0$

$\Rightarrow (a)^6 - a(a)^5 + (a)^4-a(a)^3 + 3(a)-a + 2=0$

$\Rightarrow a^6-a^6+a^4-a^4+3a-a+2=0$

$\Rightarrow 2a+2=0$

$\Rightarrow 2a=-2$

$\Rightarrow a=\frac{-2}{2}=-1$

The value of $a$ is $-1$.  

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Updated on: 10-Oct-2022

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