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

Asked by maham237 @ in Mathematics viewed by 334 People

−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

Answered by maham237 @


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.

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