Question

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

Answer 1

−1 + i times the square root of 3

is the answer.

Explanation:

Given is a quadratic equation in x

`x^2+2x+4\\= x^2+2x+1+3\\=(x+1)^2+3`

using completion of squares method

Equate to 0

`(x+1)^2+3 =0\\(x+1)^2 = -3\\`

Take square root

`(x+1) = √(-3) =±i√(3)`

Subtract one from both sides

x = [/tex]-1±i\sqrt{3}[/tex]

The last option namely

−1 + i times the square root of 3 only matches with our answre

Hence last option is right.