Final answer:
To find the zeros of the quadratic function f(x) = 9x² + 6x + 1, we use the quadratic formula. Since the discriminant (b² - 4ac) is zero, there is one real root, which is x = −(1/3).
Step-by-step explanation:
To solve for the zeros of the quadratic function f(x) = 9x + 6x + 1, we notice there might be a typo in the stated function, as it does not appear to be in standard quadratic form. Assuming the correct function is f(x) = 9x² + 6x + 1, we can solve for x using the quadratic formula:
x = −(b) ± √(b² − 4ac) / (2a)
For the equation ax² + bx + c = 0, a = 9, b = 6, and c = 1.
By plugging these values into the quadratic formula, we get:
x = −(6) ± √((6)² − 4(9)(1)) / (2(9))
x = −(6) ± √(36 − 36) / 18
x = −(6) ± √(0) / 18
x = −(6) / 18
x = −(1/3)
Therefore, the zero of this quadratic function is x = −(1/3).