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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