Question

The quadratic function f ( x ) = x 2 + 8 x + 17 is equal to zero when x = a ± b i .

Answer 1

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