Question

Which of the following is a root of the polynomial shown below?

Answer 1

Answer:

We conclude that option A is true as x = 1 is the root of the polynomial.

Step-by-step explanation:

Given the polynomial

$f\left(x\right)\:=\:x^2\:+\:2x^2\:-\:x-2$

Let us determine the root of the polynomial shown below.

$\:0=\:x^2\:+\:2x^2\:-\:x-2$

$0=3x^2-x-2$

switch sides

$3x^2-x-2=0$

as

$3x^2-x-2=\left(3x+2\right)\left(x-1\right)$

so the equation becomes

$\left(3x+2\right)\left(x-1\right)=0$

Using the zero factor principle

$3x+2=0\quad \mathrm{or}\quad \:x-1=0$

solving

$3x+2=0$

$3x=-2$

$\frac{3x}{3}=\frac{-2}{3}$

$x=-\frac{2}{3}$

and

$x-1=0$

$x=1$

The possible roots of the polynomial will be:

$x=-\frac{2}{3},\:x=1$

Therefore, from the mentioned options, we conclude that option A is true as x = 1 is the root of the polynomial.