Minimum polynomial and Isomorphic Fields

Question

I wish to show that if $α$ has minimum polynomial $t^2− 2$ over ℚ and β has minimum polynomial $t^2 − 4t + 2$ over ℚ, then the fields ℚ(α) and ℚ(β) are isomorphic. I know if $u,v$ have different minimal polynomials $p_u,p_v\in F[X]$, then $F(u)$ is not isomorphic to $F(v)$ as fields, but I am not sure about the method to prove the first statement.