Final answer:
The complex zeros of the function f(x) = 10x² + 2x + 1 are found using the quadratic formula, resulting in x = -0.1 ± 0.3i.
Step-by-step explanation:
The question asks to find the complex zeros of the quadratic function f(x) = 10x² + 2x + 1. To solve for the zeros, we can apply the quadratic formula which is x = ∛[-b ± √(b² - 4ac)]/(2a), where a, b, and c are coefficients from the quadratic equation ax² + bx + c = 0. In this case, a=10, b=2, and c=1. Plugging these values into the quadratic formula, we find that the discriminant (b² - 4ac) is less than zero, indicating that the equation has complex solutions.
Calculating the values gives us:
- √(2² - 4(10)(1)) = √(4 - 40) = √(-36)
- x = [-2 ± √(-36)] / (2*10)
- x = [-2 ± 6i] / 20
- x = -1/10 ± 3i/10
Therefore, the complex zeros of the quadratic function are x = -0.1 ± 0.3i.