Find the values of $a$ and $b$ so that $(x + 1)$ and $(x - 1)$ are factors of $x^4 + ax^3 - 3x^2 + 2x + b$.

Given:

Given expression is $x^4 + ax^3 - 3x^2 + 2x + b$.

$(x + 1)$ and $(x - 1)$ are factors of $x^4 + ax^3 - 3x^2 + 2x + b$.

To do:

We have to find the values of $a$ and $b$.

Solution:

We know that,

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

Therefore,

$f(-1)=0$

$\Rightarrow (-1)^4+a(-1)^3-3(-1)^2 + 2(-1) + b=0$

$\Rightarrow 1-a-3-2+b=0$

$\Rightarrow a=b-4$...............(i)

$f(1)=0$

$\Rightarrow (1)^4+a(1)^3-3(1)^2 + 2(1) + b=0$

$\Rightarrow 1+a-3+2+b=0$

$\Rightarrow b-4+b=0$                   [From (i)]

$\Rightarrow 2b=4$

$\Rightarrow b=\frac{4}{2}$

$\Rightarrow b=2$

$\Rightarrow a=2-4=-2$

The values of $a$ and $b$ are $-2$ and $2$ respectively.       

Tutorialspoint

Simply Easy Learning

Updated on: 10-Oct-2022

23 Views

Kickstart Your Career

Get certified by completing the course

Get Started