BY-MO 2000 Problem 1

Pit and Bill play the following game. First Pit writes down a number $a$ , then Bill writes a number $b$ , then Pit writes a number $c$ . Can Pit always play so that the three equations $$x^3+ax^2+bx+c, x^3+bx^2+cx+a, x^3+cx^2+ax+b$$ have (a) a common real root; (b) a common negative root?