# How do you find all the real and complex roots of #f(x) = x^3 + 5x^2 + 7x + 3#?

##### 1 Answer

The roots are

#### Explanation:

The graph is shown further below. It can help you guess the answers. Then we can check them as follows:

That

If you didn't have technology to help you with all this, the old-school way of doing it is to use the Rational Roots Theorem to help you in your guessing.

The fact that there are only 3 roots (counting multiplicities), and non more, is a consequence of the famed Fundamental Theorem of Algebra .

graph{x^3+5x^2+7x+3 [-5.48, 4.52, -1.94, 3.06]}