The problem asks to find one root of the equation $x^3 + 2x - 3x^2 - 6 = 0$. The possible roots are 1, -1, -3, and 3.

1. Problem Description

The problem asks to find one root of the equation $x^3 + 2x - 3x^2 - 6 = 0$. The possible roots are 1, -1, -3, and

3.

2. Solution Steps

We can test the given options to see which one satisfies the equation.

* Test $x = 1$:

$1^3 + 2(1) - 3(1)^2 - 6 = 1 + 2 - 3 - 6 = -6 \neq 0$. So, $x = 1$ is not a root.

* Test $x = -1$:

$(-1)^3 + 2(-1) - 3(-1)^2 - 6 = -1 - 2 - 3 - 6 = -12 \neq 0$. So, $x = -1$ is not a root.

* Test $x = -3$:

$(-3)^3 + 2(-3) - 3(-3)^2 - 6 = -27 - 6 - 3(9) - 6 = -27 - 6 - 27 - 6 = -66 \neq 0$. So, $x = -3$ is not a root.

* Test $x = 3$:

$3^3 + 2(3) - 3(3)^2 - 6 = 27 + 6 - 3(9) - 6 = 27 + 6 - 27 - 6 = 0$. So, $x = 3$ is a root.

Therefore, one root of the equation is $x=3$.

3. Final Answer

3