P.S. - Wolfram|Alpha
Hey Pinkk, I've gone as far as expanding the polynomial to x^72, but still have some ways to go in order to use the rational roots theorem. I'm just as clueless as to how the hell to work this out any other way, seeing as we can't assume that the sum of two irrationals is going to be irrational. I think there was some sort of underestimation as to how difficult this problem really is using the knowlege we have. I think it's just a combination of a few problems from the yellow book and was figured that it couldn't be too much harder than the others... i dunno, let me know if you make any progress, i've just about given up.
Nope, I've given up on it, it's just way too tedious and there's no guarantee that approach will work.
Edit: A professor at our college provided hints/solutions for these problems:
http://mathbin.net/38158
http://mathbin.net/38159
http://mathbin.net/38160