# Thread: real and imaginary solutions

1. ## real and imaginary solutions

find all real and imaginary solutions of f(x) = x^3 + x^2 + 13x -15

2. Originally Posted by kenzie103109
find all real and imaginary solutions of f(x) = x^3 + x^2 + 13x -15
You should be able to see that $f(1) = 1^3 + 1^2 + 13(1) - 15 = 0$.

So by the remainder and factor theorems, that means $x - 1$ is a factor.

By using long division:

$x^3 + x^2 + 13x - 15 = (x - 1)(x^2 + 2x + 15)$.

Now use the Quadratic Formula on the Quadratic factor to find the imaginary solutions.