Final answer:
The quadratic function f(x) = x² + 8x + 17 can be solved using the quadratic formula. The roots of the equation are x = -4 + i and x = -4 - i, where i is the imaginary unit.
Step-by-step explanation:
The quadratic function f(x) = x + 8x + 17 can be solved using the quadratic formula. The quadratic formula gives the solutions to a quadratic equation of the form ax + bx + c = 0 as x = (-b ± √(b^2 - 4ac))/(2a).
In this case, a = 1, b = 8, and c = 17.
Plugging these values into the formula, we get:
x = (-8 ± √(8^2 - 4 × 1 × 17))/(2 × 1)
x = (-8 ± √(64 - 68))/2
x = (-8 ± √(-4))/2
Simplifying further, we have:
x = (-8 ± 2i)/2
x = -4 ± i