Question

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

$x^3-2x^2-5x+6=0;(x=1,-2and3)$

Answer 1

Polynomial $=x^3-2x^2-5x+6$

To verify whether the values of $x$ given are the roots of polynomial or not, we can substitute the values of $x$ in polynomial and find whether it evaluates to zero. If it does, then that value will be the zero for polynomial.

For, $x=1={\left(1\right)}^3-2{\left(1\right)}^2-5\left(1\right)+6$

$=1-2-5+6$

$=0$

For, $x=-2={(-2)}^3-2{(-2)}^2-5(-2)+6$

$=-8-8+10+6$

$=0$

For, $x=3={\left(3\right)}^3-2{\left(3\right)}^2-5\left(3\right)+6$

$=27-18-15+6$

$=0$

So, all $x=1,-2,3$ are the zeroes of polynomial.

Hence, the answer verified.