The degrees of p and q must be either 1 and 4 or 2 and 3.
The given polynomial has one real root which appears irrational which rules out a degree of 1.
So let p(x) = ax^2 + bx + c
and q(x) = dx^3 + ex^2 + fx + g
It is clear that d = a = +/- 1 and c = g = +/- 1
From here one can create a system of equations relating the rest of the variables. This system, which I dont have time to explain right now, has no solutions.
Posted by Jer
on 2007-03-13 09:34:49