Posted by Praphul on Saturday, January 5, 2013 at 2:09pm.
there are 5 possible rational and real roots. Given the wording of the problem, though, it's likely that there are some complex roots, reducing the number of real candidates.
There may be 2 or 4 complex roots, meaning that there may be 5,3, or 1 real root.
Lacking any further information, all the real roots may be rational, and in fact will be integers.
A little synthetic division shows that we have no rational roots.
In fact, there are no real roots greater than 0 or less than -1. So, there are 4 complex roots and one real root -1 < r < 0