The function below has at least one rational zero.
Use this fact to find all zeros of the function.

If there is more than one zero, separate them with commas. Write exact values, not decimal approximations.

To find the rational zeros of the function , we can use the Rational Root Theorem. This theorem suggests that potential rational roots are given by the factors of the constant term (5) divided by the factors of the leading coefficient (6). The potential rational zeros, therefore, are .

By testing these values, we find that is a root of the polynomial. Next, we can perform synthetic division of the polynomial by to find the remaining roots. The result will be a quadratic polynomial.

After performing the synthetic division, we obtain:

Now, we can find the zeros of the quadratic using the quadratic formula:

Substituting , , and :

Thus, the function has the zeros:

So the final answer, listing all zeros exactly, is:

5, ,