Showing isomorphism of field extensions I need to show that if $\alpha$ has minimal polynomial $t^2-2$ over $\mathbb{Q}$ and $\beta$ has minimal polynomial $t^2-4t+2$ over $\mathbb{Q}$, then the extensions $\mathbb{Q}(\alpha):\mathbb{Q}$ and $\mathbb{Q}(\beta):\mathbb{Q}$ are isomorphic. 
I want to say that somehow $t^2-2 \equiv t^2-4t+2$ modulo something and this will be of help in the proof? I see that $t^2-4t+2-(t^2-2)=-4t+4$, so maybe I should work modulo $1-t$? Does this make any sense and am I on the right track? 
Thanks.

Write $\Bbb Q(\alpha)\cong\Bbb Q[t]/(t^2 - 2)$ and $\Bbb Q(\beta)\cong\Bbb Q[x]/(x^2 -4x + 2)$. The roots of $t^2 - 2$ are $\pm\sqrt{2}$ and the roots of $t^2 - 4t + 2$ are $2\pm\sqrt{2}$. Since $t$ in the first quotient represents $\sqrt{2}$ or $-\sqrt{2}$, and $x$ in the second represents either $2 + \sqrt{2}$ or $2 - \sqrt{2}$, does this tell you where to send $t$ to define a map $\Bbb Q[t]/(t^2 - 2)\to\Bbb Q[x]/(x^2 - 4x + 2)$?
