Difference between revisions of "2017 AMC 12A Problems/Problem 19"

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-==Problem==
-A set <math>S</math> is constructed as follows. To begin, <math>S = \{0,10\}</math>. Repeatedly, as long as possible, if <math>x</math> is an integer root of some polynomial <math>a_{n}x^n + a_{n-1}x^{n-1} + ... + a_{1}x + a_0</math> for some <math>n\geq{1}</math>, all of whose coefficients <math>a_i</math> are elements of <math>S</math>, then <math>x</math> is put into <math>S</math>. When no more elements can be added to <math>S</math>, how many elements does <math>S</math> have?
-<math> \textbf{(A)}\ 4
-\qquad \textbf{(B)}\ 5
-\qquad\textbf{(C)}\ 7
-\qquad\textbf{(D)}\ 9
-\qquad\textbf{(E)}\ 11</math>

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