Final answer:
The quadratic equation f(x) = x^2 + 4x + 8 has a discriminant of -16, indicating no real roots. The quadratic formula shows that the equation's solutions are two complex numbers: -2 + 2i and -2 - 2i. The given options do not correspond to these correct solutions.
Step-by-step explanation:
To find the zeros of the quadratic equation f(x) = x^2 + 4x + 8, we need to use the quadratic formula, which is:
x = (-b ± √(b^2 - 4ac))/(2a)
The discriminant of the quadratic equation is given by b^2 - 4ac. In this case, a = 1, b = 4, and c = 8.
The discriminant is therefore (4)^2 - 4(1)(8) = 16 - 32 = -16. Since the discriminant is negative, this quadratic equation does not have real solutions and thus the square root will involve imaginary numbers.
Your completed statement should say:
- The value of the discriminant in this equation is equal to the square root of -16.
- After substituting into the Quadratic Formula, the numerator would be -4.
- After substituting into the Quadratic Formula, the denominator would be 2.
- Finally, after simplifying, our two solutions to the equation would be -2 + 2i and -2 - 2i.
None of the given options (A, B, C, D) provide the correct numbers for the discriminant, the numerator, the denominator, or the two solutions. Therefore, we can conclude that the solutions to the quadratic equation f(x) = x^2 + 4x + 8 are complex numbers, specifically -2 + 2i and -2 - 2i.