D. x^2 - 2x - 4 = 0
You can solve this problem 2 different ways.
1. Plug in a value of x = 1 ± √5 into each of the possible equations and see if the result is 0.
or
2. Use the Quadratic formula to solve each of the equations and see which comes up with the correct answer.
For this case, I'll use the 2nd option.
A. x^2 + 2x + 4 = 0
a = 1, b = 2, c = 4
Upon attempting this, you'll quickly discover that you're going to try to get the square root of -12. Since there's no imaginary terms in the desired root, this equation can't be it.
B. x^2 – 2x + 4 = 0
Same issue here, trying to get the square root of a negative number. So this one doesn't work either.
C. x^2 + 2x – 4 = 0
Getting closer. Have (-2 ± sqrt(20)) / 2 = -1 ± √5
Still not it, but closer. At least not trying to get the square root of a negative number.
D. x^2 – 2x – 4 = 0
Since the other 3 are wrong, this must be right. But let's do the math anyway.
a = 1, b = -2, c = -4
The quadratic formula gets (2 ± sqrt(20)) / 2 = (2 ± 2√5)/2 = 1 ± √5
And it works out. So this is the answer.