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.