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What is the value of B in the equation Ax^2 + Bx + C = 0, where A, B, C are integers.
1. Product of the roots is 16.
2. One root is 4 times the other.

The question is to find out the value of 'B' in the given quadratic equation.

We can find a unique value for B, if we know the roots of the quadratic equation.

Let the roots be 'p' and 'q'. We have to find out if the information provided in the two statements is sufficient to find a unique pair of values for 'p' and 'q'.

Statement 1: The product of the roots is 16. Multiple possibilities exist. p could be 1, q could be 16 or p could be 8 and q could be 2 or p could be -8 and q could be -2 and so on. So, statement 1 is not sufficient.

Statement 2: One root is 4 times the other. p = 4q. Multiple possibilities. Hence, statement 2 alone is not sufficient.

Let us combine the information in the two statements.
We have pq = 16 and p = 4q. Sustituting p = 4q in the first equation, we get 4q^2 = 16.
Or q^2 = 4 or q = +2 or -2.

As we cannot find a unique value for q and therefore, for p, we will not be able find a unique value for B.

Hence, choice E is the correct answer.