Question

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

f(x) = x2 + 2x2 - x-2
O A. 1
OB. 3
O c. O
O D. 2

Answer 1

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

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`

`(3x)/(3)=(-2)/(3)`

`x=-(2)/(3)`

and

`x-1=0`

`x=1`

The possible roots of the polynomial will be:

`x=-(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.