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 polynomial , we can use the Rational Root Theorem. This theorem states that any potential rational zero, in the form of , is derived from the factors of the constant term and the leading coefficient. Here, the factors of 7 (constant term) are and the factors of 5 (leading coefficient) are . Therefore, the potential rational zeros to test are .

Testing :

Testing :

Since is a zero, we can factor using synthetic division to find the other roots.

Using synthetic division:

-1/5 |  5   12   12   7
      |     -1   -11  -7
-------------------------
        5   11   1   0

This gives us . We can now solve using the quadratic formula:

Thus, the zeros of the function are: