Solve for the zeros of the quadratic function f (x) = 9x2 + 6x + 1. Write the answer as a fraction.

We are asked to solve for the zeros of the given quadratic equation f (x) = 9x2 + 6x + 1. To solve this, first, we need to set the given equation into zero such as the succeeding solution is shown below:

0 = 9x2 + 6x + 1

Perform factoring such as:

0 = (3x + 1) (3x + 1)

Solving for x1, we have:

3x + 1=0

3x = - 1

x1 = - 1/3

Soving for x2, we have:

3x + 1=0

x = - 1/3

Therefore, the zeroes of the given expression is both - 1/3 for x1 and x2.