Question

Which of the following is a solution of x^2 + 2x + 8?

4 + i times the square root of 7
−1 + i times the square root of 7
2 + i times the square root of 7
−4 + i times the square root of 7

Answer 1

x^2 + 2x + 8 = 0
x^2 + 2x = -8
x^2 + 2x + 1 = -8 + 1
(x + 1)^2 = -7
x + 1 = (+-) sqrt -7
x = -1 (+-) sqrt -7

solution is : x = -1 + i * sqrt 7