Final answer:
The complex zeros of the quadratic function f(x) = 5x² - 4x + 1 are found using the quadratic formula. The zeros are x = 0.4 + 0.2i and x = 0.4 - 0.2i after substituting a = 5, b = -4, and c = 1 into the formula.
Step-by-step explanation:
The complex zeros of the quadratic function f(x) = 5x² - 4x + 1 can be found using the quadratic formula. The formula is given by x = [-b ± √(b² - 4ac)] / (2a), where a, b, and c are coefficients from the quadratic equation of the form ax² + bx + c = 0.
For the given function, a = 5, b = -4, and c = 1. Plugging these values into the quadratic formula we get:
x = [4 ± √((-4)² - 4(5)(1))] / (2(5))
x = [4 ± √(16 - 20)] / 10
x = [4 ± √(-4)] / 10
x = [4 ± 2i] / 10
x = 0.4 ± 0.2i
Therefore, the complex zeros of the quadratic function are x = 0.4 + 0.2i and x = 0.4 - 0.2i.