Final answer:
The discriminant for the quadratic equation h² + 2h + 3 is negative, indicating there are no real solutions but two complex solutions.
Step-by-step explanation:
To determine the number of solutions to the quadratic equation h² + 2h + 3 = 0, we use the discriminant method. The discriminant is found by using the formula b² - 4ac, where a, b, and c are coefficients from the quadratic equation ax² + bx + c = 0. In this case, a = 1, b = 2, and c = 3.
The discriminant for this equation would be (2)² - 4(1)(3) = 4 - 12 = -8. Since the discriminant is negative, it indicates that there are no real number solutions and two complex solutions