Explanation

This gives us a quadratic equation and wants us to tell it about whether the roots are positive. If the entities b and c here were numbers, we could factor the quadratic equation in order to solve it and find the roots directly. In that case, we would write



Precisely the question at hand is whether the question marks are to be populated by positive or by negative numbers. The two question-mark numbers will have to add to give us b and multiply to give us c, as you may recall and as you can see by imagining a case. Given all that, let's turn to the statements, separately first.

Statement (1) tells us that b is negative. That means the roots must sum to a negative number. That means, in one case, one of them might be positive and one negative. In other case, both might be negative. But they cannot both be positive--otherwise they wouldn't sum to a negative number. Therefore we can definitively answer the question posed, in the negative. Statement (1) is sufficient.

Statement (2) tells us that c is negative. Since c is the product of the two roots, that means that one of the roots must be positive one and one negative; it's the only way to get a negative product, since a positive times a positive is a positive and a negative times a negative is a positive. Therefore, we can answer the question posed with a definitive "no." Statement (2) is sufficient.

The correct answer is (D).