Question

Verify Whether the following are roots of the polynomial equations indicated against them.

$x^3-2x^2-x+2=0;(x=-1,2and3)$

Answer 1

$x^3-{2x}^2-x+2$

$\Rightarrow$ For $x=-1$

$\Rightarrow {(-1)}^3-2{\left(1\right)}^2-(-1)+2=-1-2+1+2=0$

Hence, $x=-1$ is a zero of polynomial

Similarly, for $x=2$

$\Rightarrow {\left(2\right)}^3-2{\left(2\right)}^2-\left(2\right)+2=0$

So, $x=2$ is also a zero.

For $x=3$

$\Rightarrow {\left(3\right)}^3-2{\left(3\right)}^2-\left(3\right)+2=27-18-3+2\ne 0$

Hence, $x=3$ is not a zero.

Hence, verified.