1984 AHSME Problem 16

The function f(x) satisfies f(2+x)=f(2-x) for all real numbers x. If the equation f(x)=0 has exactly four distinct real roots, then the sum of these roots is

\mathrm{(A) \ }0 \qquad \mathrm{(B) \ }2 \qquad \mathrm{(C) \ } 4 \qquad \mathrm{(D) \ }6 \qquad \mathrm{(E) \ } 8

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