2003 AMC 12A Problem 21

The graph of the polynomial

P(x) = x^5 + ax^4 + bx^3 + cx^2 + dx + e

has five distinct x-intercepts, one of which is at (0,0). Which of the following coefficients cannot be zero?

\textbf{(A)}\ a \qquad \textbf{(B)}\ b \qquad \textbf{(C)}\ c \qquad \textbf{(D)}\ d \qquad \textbf{(E)}\ e

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.