Consider the quadratic equation nx2 + 7nx + n = 0 , where n is a positive integer. Which of the following statements are necessarily correct ?
I. For any n, the roots are distinct.
II. There are infinitely many values of n for which both roots are real.
III. The product of the roots is necessarily an integer.
(A) III only
(B) I and III only
(C) II and III only
(D) I, II and III
