solve: $x^2 + 2x + 17 = 0$ \na $x = -1 + 4i$ or $x = -1 - 4i$ \nb $x = -1 + 8i$ or $x = -1 - 8i$ \nc $x = 1…

Explanation:

Step1: Identify the quadratic formula

For a quadratic equation (ax^2 + bx + c = 0), the solutions are given by (x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}). Here, (a = 1), (b = 2), and (c = 17).

Step2: Calculate the discriminant

The discriminant is (b^2 - 4ac). Substituting the values, we get (2^2-4\times1\times17 = 4 - 68=-64).

Step3: Find the square root of the discriminant

(\sqrt{-64}=\sqrt{64}\times\sqrt{-1}=8i) (since (\sqrt{-1}=i)).

Step4: Apply the quadratic formula

Substitute into the quadratic formula: (x=\frac{-2\pm8i}{2\times1}=\frac{-2\pm8i}{2}=-1\pm4i).

Answer:

A. (x = -1 + 4i) or (x = -1 - 4i)