Question

Verify whether the following are roots of the polynomial equations indicated against them.
$2x^2-3x-2=0;x=2,3$

Answer 1

Let $p\left(x\right)=2x^2-3x-3$
$p\left(p\right)=2(2{)}^2-3(2)-2=8-6-2=0$
Hence, x=2 is root of $x^2-3x-2=0$
But $p\left(3\right)=2(3{)}^2-3(3)-2=18-9-2=7\ne 0$
Hence, x=3 is not a root of $2x^2-3x-2=0$