Problem: The equation 2000x6+100x5+10x3+x−2=02000x^6+100x^5+10x^3+x-2=02000x6+100x5+10x3+x−2=0 has exactly two real roots, one of which is m+nr\frac{m+\sqrt{n}}rrm+n, where mmm, nnn and rrr are integers, mmm and rrr are relatively prime, and r>0r>0r>0. Find m+n+rm+n+rm+n+r.
Solution:
The problems on this page are the property of the MAA's American Mathematics Competitions