Question

Find all roots: x^3 + 7x^2 + 12x = 0
Show all work and check your answer.

Answer 1

`x=0,x=-4,x=-3`

Explanation:

The given equation is

`x^3 + 7x^2 + 12x = 0`

Factoring by x:

`(x^2 + 7x + 12)x = 0`

One of the root is x=0. Let's solve the parentheses.

Expanding the trinomial

`x^2 + 4x+3x + 12=0`

Factoring

`x(x + 4)+3(x + 4)=0`

Factoring

`(x + 4)(x+3)=0`

This will give us the two remaining roots

`x=-4,x=-3`