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2003 AMC 12A Question 21

AMC12 · 2003 AMC 12A

Question 21

The graph of the polynomial $$
\begin{aligned} &P(x) = x^5 + ax^4 + bx^3 \\ &\quad {}+ cx^2 + dx + e \end{aligned}
$$

has five distinct $x$-intercepts, one of which is at $(0, 0).$ Which of the following coefficients cannot be zero?
  1. $a$
  2. $b$
  3. $c$
  4. $d$
  5. $e$