Find value of $a$ if $x+1$ is a factor of $x^3-ax^2+6x-a$.

Given:

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

$x + 1$ is a factor of $x^3-ax^2+6x-a$.

To do:

We have to find the value of $a$.

Solution:

If $(x-m)$ is a root of $f(x)$ then $f(m)=0$.

This implies,

$(x+1)=x-(-1)$

Therefore,

$f(x)=x^3 - ax^2 + 6x - a$

$f(-1)=0$

$\Rightarrow (-1)^3-a(-1)^2+6(-1)-a=0$

$\Rightarrow -1-a-6-a=0$

$\Rightarrow -2a-7=0$

$\Rightarrow 2a=-7$

$\Rightarrow a=\frac{-7}{2}$

The value of $a$ is $\frac{-7}{2}$. 

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Updated on: 10-Oct-2022

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