Problem Solving

Hmmm, I'm not too sure about this one.

The question suggests that, for each non-zero value of b, the function will always yields the least possible value when x has a particular value.
So, I chose an easy value for b. I let b = 1

If b = 1, then the function becomes f(x) = x² + 2x + 4
Now let's test each answer choice to see which value of x yields the smallest output.

A) x = -1 - √(1 - 4b)
If b = 1, then x = -1 - √(1 - 4(1)) = -1 - √(-3)
Since we can't find the value of √(-3), x has no real value. So, we can't even plug it into f(x)
[on the GMAT, we use real numbers only. In other words, we don't use complex/imaginary numbers]

B) x = -2
f(-2) = (-2)² + 2(-2) + 4 = 4

C) x = 0
f(0) = (0)² + 2(0) + 4 = 4

D) x = -b²
Since we've let b = 1, we get x = -(1²) = -1
So, f(-1) = (-1)² + 2(-1) + 4 = 3

E) x = b - 4
Since we've let b = 1, we get x = (1) - 4 = -3
So, f(-3) = (-3)² + 2(-3) + 4 = 7

So, when b = 1, the function outputs the smallest value when x = -b²
So, IT SEEMS that the answer should be D

HOWEVER, as you mentioned, if we let b = -2, then the function yields an output of 0 when x = -1 - √(1 - 4b) (answer choice A) and the function yields an output of 0 when x = -b² (answer choice D). So, it looks like A and D are both correct.

So, unless I'm missing something here, I think this question misses the mark. What's the source?

Cheers,
Brent