Question

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

Answer 1

Equation $\to x^4+a{x}^3+2x^2-3x+b...\left(1\right)$

$(x+1)$ and $(x-1)$ are roots of the equation.

So, $x=-1$ and $x=1$

Put $x=-1$ in equation (1)

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

$a-b=6...\left(2\right)$

Put $x=1$ in equation (1)

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

$a+b=0...\left(3\right)$

Add equation (2) & equation (3)

$2a=6$

$a=3$

Put $a=+3$ in equation (2)

$b=-3$