**Quote:**

If b and c are constants for which the quadratic equation \(x^2+bx+c=0\) has two different roots, what is the product of the two roots?

(1) One of the roots is 3.

(2) c=6

We are given that the quadratic equation x^2 + bx + c = 0 has two different roots. We need to determine the product of these two roots.

Recall that in a quadratic equation in the form ax^2 + bx + c = 0, the sum of the two roots is –b/a and the product of the two roots is c/a. Here, we are given the equation in the form of x^2 + bx + c = 0, and since a = 1, the product of the two roots is c/1 = c.

Thus, if we know the value of c, then we know the product of the two roots.

Statement One Alone:

One of the roots is 3.

We are given that one of the roots is 3. However, since we don’t know the value of the other root, we can’t determine the product of the two roots. Statement one alone is not sufficient. Eliminate choices A and D.

Statement Two Alone:

c = 6

Since we know the value of c, the product of the two roots must be 6 (see problem stem analysis above). Statement two alone is sufficient.

Answer: B

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