2007 AMC 12A Problem 21

The sum of the zeros, the product of the zeros, and the sum of the coefficients of the function f(x)=ax^{2}+bx+c are equal. Their common value must also be which of the following?

\textrm{(A)}\ \textrm{the\ coefficient\ of\ }x^{2}~~~ \textrm{(B)}\ \textrm{the\ coefficient\ of\ }x \textrm{(C)}\ \textrm{the\ y-intercept\ of\ the\ graph\ of\ }y=f(x) \textrm{(D)}\ \textrm{one\ of\ the\ x-intercepts\ of\ the\ graph\ of\ }y=f(x) \textrm{(E)}\ \textrm{the\ mean\ of\ the\ x-intercepts\ of\ the\ graph\ of\ }y=f(x)

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