1984 AIME Problem 12

A function f is defined for all real numbers and satisfies f(2+x)=f(2-x) and f(7+x)=f(7-x) for all x. If x=0 is a root for f(x)=0, what is the least number of roots f(x)=0 must have in the interval -1000\leq x \leq 1000?

Leading zeroes must be inputted, so if your answer is 34, then input 034

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