Explanation:
To solve for the zeros of a quadratic function, we need to find the values of x where f(x) equals zero. This means that we need to set the quadratic function equal to zero and solve for x.
In this case, our quadratic function is f(x) = 9x² + 6x + 1. To set it equal to zero, we write:
9x² + 6x + 1 = 0
Now we can use the quadratic formula to solve for x:
x = (-b ± √b² - 4ac) / 2a
In this equation, a, b, and c are the coefficients of the quadratic function. In our case, a = 9, b = 6, and c = 1. Substituting these values into the equation, we get:
x = (-6 ± √36 - 4(9)(1)) / 2(9)
Simplifying, we get:
x = (-6 ± √0) / 18
Since the square root of 0 is 0, we have:
x = -6/18 and x = -6/18
Reducing the fractions, we get:
x = -1/3 and x = -1/3
Therefore, the zeros of the quadratic function f(x) = 9x² + 6x + 1 are x = -1/3 and x = -1/3.