# How do you use the rational root theorem to find the roots of # f(x) = 3x^3 + 7x^2 + 11x + 5#?

##### 1 Answer

Oct 21, 2015

Find all the factors of 5 and 3, then try them to see if they are roots

#### Explanation:

The rational root theorem states that the ratio of the factors of the constant term (5) divided by the coefficient on the highest exponent (3) **might** result in rational roots to the equation.

**Possible rational roots** :

Unfortunately, none of these actually work as a solution.

Using a graphing calculator, I find only one real root

The other two roots are imaginary.

Note: The **Descartes Rule of Signs** shows that there are no **positive** solutions and either 1 or 3 **negative** solutions.

Hope that helped