Choice A is the correct answer. Calculate the discriminant $\Delta = b^2 - 4ac$.

1. $\Delta = (-12)^2 - 4(4)(9)$.
2. $\Delta = 144 - 144 = 0$.
3. Since $\Delta = 0$, there is exactly one real repeated root.

Choice B is incorrect because $\Delta$ is not positive. Choice C is incorrect because $\Delta$ is not negative. Choice D is incorrect because roots come in conjugate pairs.