Question

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

Answer 1

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 :

`+-1/1,5/1,1/3, 5/3`

Unfortunately, none of these actually work as a solution.

Using a graphing calculator, I find only one real root `x ~~-0.64713`

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