2019 CIME I Problems/Problem 13
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Suppose 
is a monic polynomial whose roots 
, 
, and 
are real numbers, at least two of which are positive, that satisfy the relation ![\[a(a-b)=b(b-c)=c(c-a)=1.\]](http://latex.artofproblemsolving.com/0/c/6/0c6a3f7640b22ddcf9dec7311e7432a55608db52.png)
Find the greatest integer less than or equal to ![\[100|P(\sqrt{3})|\]](http://latex.artofproblemsolving.com/7/f/a/7fae63129ffaa489d0160772778c584ca703aa6f.png)
.
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