Final answer:
To find the zeros of the function f(x) = 2x^2 - 8x + 17, use the quadratic formula and solve the equation 2x^2 - 8x + 17 = 0. The zeros of the function are the values of x that make the equation true.
Step-by-step explanation:
To find the zeros of the function f(x) = 2x^2 - 8x + 17, we need to solve the equation 2x^2 - 8x + 17 = 0. Using the quadratic formula, x = (-b ± √(b^2 - 4ac)) / 2a, where a = 2, b = -8, and c = 17. Plugging in these values, we get:
x = (-(-8) ± √((-8)^2 - 4(2)(17))) / (2(2))
x = (8 ± √(64 - 136)) / 4
x = (8 ± √(-72)) / 4
Since the expression inside the square root is negative, there are no real solutions. Therefore, the correct answer is D) There are no real solutions.