Let f 6 (CM be a monic polynomial of degree n 2 1. (a) If f has n distinct roots in (C, prove that CM / ( f ) E C\". (Here C\" means the direct product of n copies of (C, as a ring.) (b) If f has any multiple roots, show that (C[:c]/ (f) contains a nonzero nilpotent element, that is, a nonzero element t such that tk = 0 for some k 2 2. Conclude that (C[:c]/ (f ) is not isomorphic to C\