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 anxn+an−1xn−1+⋯+a1x+a0 for some n≥1, all of whose coefficients ai 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?<spanclass=′latex−bold′>(A)</span>4<spanclass=′latex−bold′>(B)</span>5<spanclass=′latex−bold′>(C)</span>7<spanclass=′latex−bold′>(D)</span>9<spanclass=′latex−bold′>(E)</span>11