let say i have P_1(x)= x^2+ x + \alpha as irreducible polynomial over GF(2^2) to construct GF((2^2)^2). and P_2(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??