Bunuel wrote:

x^2 + bx + 72 = 0 has two distinct integer roots; how many values are possible for b?

A. 3

B. 6

C. 8

D. 12

E. 24

For a quadratic equation ax^2+bx+c=0, we know that -b/a is sum of roots and c/a is product of roots.

The quadratic equation here is x^2 + bx + 72 = 0, where product of roots is 72.

If we find all the factors of 72, we have the answer.

By prime factorization, we get 72= 2^3*3^2.

We know that total factors are (3+1)*(2+1) = 12 (Reason: with 2^n, we have n+1 possibilities. n^0 to n^n. so n+1)

Anees Shaik.