For what value of $a, (x - 5)$ is a factor of $x^3 - 3x^2 + ax - 10$?

Given:

Given expression is $x^3-3x^2+ax-10$.

$x - 5$ is a factor of $x^3-3x^2+ax-10$.

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,

$f(5)=0$

$\Rightarrow (5)^3-3(5)^2+a(5)-10=0$

$\Rightarrow 125-75+5a-10=0$

$\Rightarrow 5a+40=0$

$\Rightarrow 5a=-40$

$\Rightarrow a=\frac{-40}{5}=-8$

The value of $a$ is $-8$.  

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Updated on: 10-Oct-2022

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