Final answer:
The roots of the quadratic equation x^2 + 4x + 8 = 0 are found using the quadratic formula. They are complex numbers, -2 + 2i and -2 - 2i, which corresponds to option C).
Step-by-step explanation:
To find the roots of the quadratic equation x^2 + 4x + 8 = 0, we can use the quadratic formula, which is given by:
x = [-b ± √(b^2-4ac)] / (2a)
In this equation, a = 1, b = 4, and c = 8. Plugging these values into the quadratic formula, we get:
x = [-4 ± √(4^2 - 4*1*8)] / (2*1)
x = [-4 ± √(16 - 32)] / 2
x = [-4 ± √(-16)] / 2
Since the square root of a negative number results in an imaginary number, we can rewrite √(-16) as 4i (where i is the imaginary unit).
Therefore:
x = [-4 ± 4i] / 2
x = -2 ± 2i
Thus, the roots of the equation are -2 + 2i and -2 - 2i, which corresponds to option C).