prove that x^6 - x^2 + 2 has no constructible roots

First, i let y=x^2, so the function become y^3 - y + 2

then use the theorem, if polynomial f(x) has integer coefficient and a ration root p/q. (p,q)=1, then p|a0 , q|an.

I got p|2 and q|1

g(2) does not equal to zero.

so. the function does not have a rational root.

How do I go on from here..