A set S is constructed as follows. To begin, S=\{0,10\}. Repeatedly, as long as possible, if x is an integer root of some polynomial a_{n} x^{n}+ a_{n-1} x^{n-1}+\cdots+a_{1} x+a_{0} for some n \geq 1, all of whose coefficients a_{i} are elements of S, then x is put into S. When no more elements can be added to S, how many elements does S have?
Answer Choices
A. 4
B. 5
C. 7
D. 9
E. 11