Question

If $x=2$ and $x=0$ are root of polynomial $f\left(x\right)=2x^3-5x^2+ax+b$. Find the value of $a$ and $b$.

Answer 1

Let, $f\left(x\right)=2x^3-5x^2+ax+b$

Since $x=2$ is a root of $f\left(x\right)$.

$\therefore f\left(2\right)=0$

$\Rightarrow 16-20+2a+b=0$

$\Rightarrow 2a+b=4$............(1)

Also $x=0$ is a root of $f\left(x\right)$

$\therefore f\left(0\right)=0$

$\Rightarrow b=0$.............(2)

Using (2) in equation (1) we get,

$a=\frac{4}{2}$ $=2$

$\therefore a=2$ and $b=0$.