Math Help - Rational Root Theorem for polynomials...

1. Rational Root Theorem for polynomials...

Given n E N, find a p(x) E q(x) of degree n which has no rational roots..

where standard polynomial equation is:
P(x) = (c_n)x^n + (c_n-1)x^n-1 + (c_n-2)x^n-2+....(c_1)x^1 + C_o

and similarly we may assume the polynomial equation for q(x) using 'm' in terms of 'n'....

2. The polynomial $x^n - 2$ never has a rational root when $n\geq 2$.

3. I am sorry, I guess the description was not clear. I meant for x^(n-1), x^(n-2), x^(n-3)....and so on...

this is not given..but I guess this might be the standard way of writing any polynomial and I got it from wikipedia...
I hope that helps to help me...