1998 Cayley Problem 21

When Betty substitutes x=1 into the expression ax^3-2x+c its value is -5. When she substitutes x=4 the expression has value 52. One value of x that makes the expression equal to zero is

\textbf{(A)}\ 2\quad \textbf{(B)}\ \frac{5}{2}\quad \textbf{(C)}\ 3\quad \textbf{(D)}\ \frac{7}{2}\quad \textbf{(E)}\ 4

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.