Let f(x) = x3 + px2 + qx + r, where p,q and r are integers, f(0) and f(-1) are odd integers. Which of the following is/are CORRECT ?
(A) f(1) is an even integer
(B) f(1) is an odd integer
(C) f(x) = 0 has three distinct integer roots
(D) f(x) = 0 cannot have three integer roots