Difference between revisions of "2017 AMC 12A Problems/Problem 19"
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==Problem== | ==Problem== | ||
| − | 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>. | + | 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>. When no more elements can be added to <math>S</math>, how many elements does <math>S</math> have? |
<math> \textbf{(A)}\ 4 | <math> \textbf{(A)}\ 4 | ||
Revision as of 17:07, 8 February 2017
Problem
A set 
is constructed as follows. To begin, 
{
}. Repeatedly, as long as possible, if 
is an integer root of some polynomial 
for some 
, all of whose coefficients 
are elements of , then is put into . When no more elements can be added to , how many elements does have?
