## Irreducible polynomial

let say i have P1(x)= x^2+ x + \alpha as irreducible polynomial over GF(2^2) to construct GF((2^2)^2). and P2(x) = x^2+ x + \beta as irreducible polynomial over GF((2^2)^2) to construct GF(((2^2)^2)^2).

if i have \alpha = {10}2 or {11}2 , what are the possible value for \beta in order to be irreducible??