How do you solve 9x ^ { 4} + 18x ^ { 3} + 9x ^ { 2} = 0?

1 Answer
Oct 25, 2017

x = -1, -1, 0, 0

Explanation:

First, begin by factoring as much as possible from each term of the equation on the left hand side:

9x^4 + 18x^3 + 9x^2 = 0

(9x^2)(x^2 + 2x + 1) = 0

Now factor the quadratic:

(9x^2)(x+1)(x+1) = 0

Since we know the product of the three terms on the left comes out to 0, we know that any one of those terms evaluating to 0 will be a solution of the equation. Thus, we solve each factor separately to determine all possible solutions for x:

9x^2 = 0

x^2 = 0

x = +- 0 => x = 0 " (Multiplicity 2)"

x+1 = 0 => x = -1

x + 1 = 0 => x = -1

We get four roots: x = -1, -1, 0, 0.