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

Revision as of 18:06, 8 February 2017

Problem

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 $a_{n}x^n + a_{n-1}x^{n-1} + ... + a_{1}x + a_0$ for some $n\geq{1}$ , all of whose coefficients $a_i$ are elements of $S$ , then $x$ is put into $S$ .

$\textbf{(A)}\ 4 \qquad \textbf{(B)}\ 5 \qquad\textbf{(C)}\ 7 \qquad\textbf{(D)}\ 9 \qquad\textbf{(E)}\ 11$

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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>.
+A set <math>S</math> is constructed as follows. To begin, <math>S = </math>{<math>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>.
 <math> \textbf{(A)}\ 4

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

Revision as of 18:06, 8 February 2017

Problem