Question

If $(2x-3)$ is a factor of $2x^3-9x^2+x+k$ then find value of $k$.

Answer 1

Let $g\left(x\right)=2x-3$

Zero of $g\left(x\right)\Rightarrow 2x-3=0\Rightarrow x=3/2$

$\therefore {f\left(3/2\right)=2\left(3/2\right)}^3-9{\left(3/2\right)}^2+\frac{3}{2}+k.$

$=\frac{27}{2}-\frac{81}{4}-\frac{3}{2}+k.$

$\therefore (2x-3)$ is a factor of $f\left(x\right)$

$\therefore f\left(x\right)=0\Rightarrow f\left(3/2\right)=0$

or, $\frac{27}{4}-\frac{81}{4}+\frac{3}{2}+k=0.$

or, $\frac{-54}{4}+\frac{3}{2}+k=0.$

or, $\frac{-54+6}{4}+k=0.$

or, $k=\frac{48}{4}\Rightarrow k=12$