Choice A is the correct answer.

1. Product Rule: Product = 12. One root is 4, so the other root must be $12/4 = 3$.
2. Sum Rule: Sum = $4 + 3 = 7$.
3. Coefficient: The linear coefficient $b$ is the negative of the sum. So $b = -7$.

Alternatively, substitute $x=4$: $16 + 4b + 12 = 0 \Rightarrow 4b = -28 \Rightarrow b = -7$.

Choice B is incorrect because of sign error. Choice C is incorrect. Choice D is incorrect because it is the other root.