Which of the following is a solution of x2 + 2x + 4?

-2 + two i times the square root of 3

2 + two i times the square root of 3

1 - i times the square root of 3

-1 + i times the square root of 3

Strictly speaking, x^2 + 2x + 4 doesn't have solutions; if you want solutions, you must equate x^2 + 2x + 4 to zero:

x^2 + 2x + 4 = 0. "Completing the square" seems to be the easiest way to go here:

rewrite x^2 + 2x + 4 as x^2 + 2x + 1^2 - 1^2 = - 4, or

(x+1) ^2 = - 3

or x+1 = i * (plus or minus sqrt (3))

or x = - 1 plus or minus i*sqrt (3)

This problem, like any other quadratic equation, has two roots. Note that the fourth possible answer constitutes one part of the two part solution found above.