Final answer:
The quadratic relation f(x) = x² + 2x + 2 has zero real zeros or solutions because the discriminant, calculated as b² - 4ac, yields a negative number, indicating that all solutions are complex.
Step-by-step explanation:
To determine how many zeros (solutions) the quadratic relation f(x) = x² + 2x + 2 has, we need to assess the discriminant of the quadratic equation, which is b² - 4ac. For this equation, a = 1, b = 2, and c = 2. Calculating the discriminant, we have (2)² - 4(1)(2) = 4 - 8 = -4.
Since the discriminant is negative, there are no real solutions to this quadratic equation; it has zero real zeros. However, there will be two complex solutions. Quadratic equations of the form ax² + bx + c = 0 can typically be solved using the quadratic formula, but in this case, the negative discriminant indicates the solutions are not real numbers.