We are asked to find all the roots of the equation $x^3 + 11x^2 + 28x = 0$.

1. Problem Description

We are asked to find all the roots of the equation $x^3 + 11x^2 + 28x = 0$.

2. Solution Steps

First, we can factor out an $x$ from the equation:

$x(x^2 + 11x + 28) = 0$

Now we need to factor the quadratic expression $x^2 + 11x + 28$. We are looking for two numbers that multiply to 28 and add up to

1

1. Those numbers are 4 and

7. So we can factor the quadratic as:

$x^2 + 11x + 28 = (x+4)(x+7)$

Thus, the original equation can be written as:

$x(x+4)(x+7) = 0$

The roots are the values of $x$ that make the equation equal to zero. Therefore, the roots are $x=0$, $x=-4$, and $x=-7$.

3. Final Answer

The roots are $x = 0, -4, -7$.