There are 4 solutions to the problem posed.
If we ignore the +1 the polynomial clearly has a root at each of 1...20
Noting its end behavior we know it has local minima in each of (1,2),(3,4)...(19,20).
If you shift the polynomial up 1 unit, the roots will either:
1). Move inward a bit.
2). Move inward and become a double root.
3). Become nonreal.
Because each of the minima between the roots are so low (thousands at least) option 1). Occurs each time.
So there are four solutions: two each on (9,10) and (11,12).

Posted by Jer
on 20130914 13:14:44 