Question

If $(x-4)$ is a factor of $x^3+a{x}^2+2bx-24$ and $a-b=8$; find the values of $a$ and $b$.

Answer 1

$(x-4)$ is a factor of $x^3+a{x}^2+2bx-24$

$(4{)}^3+a(4{)}^2+2b\left(4\right)-24=0$

$⟹64+16a+8b-24=0$

$⟹16a+8b=-40-------\left(1\right)$

and given, $a-b=8--------\left(2\right)$

eqn(1) can be further divided by $8$ ,we get

$2a+b=-5--------\left(3\right)$

Solving $\left(2\right)\&\left(3\right)$, we get

$3a=3$

$⟹a=1$

$⟹b=-7$