If $x - 2$ is a factor of each of the following two polynomials, find the values of $a$ in each case:$x^3 - 2ax^2 + ax - 1$

Given:

Given expression is $x^3 - 2ax^2 + ax - 1$

$x - 2$ is a factor of $x^3 - 2ax^2 + ax - 1$.

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,

$f(2)=0$

$\Rightarrow (2)^3 - 2a(2)^2 + a(2) - 1=0$

$\Rightarrow 8-8a+2a-1=0$

$\Rightarrow 7-6a=0$

$\Rightarrow 6a=7$

$\Rightarrow a=\frac{7}{6}$

The value of $a$ is $\frac{7}{6}$.

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Updated on: 10-Oct-2022

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