AMC 12 2003a 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 \textbf{(B)}\ b \textbf{(C)}\ c \textbf{(D)}\ d \textbf{(E)}\ e