Is $\mathbb{Q}(t):\mathbb{Q}$ a normal field extension?

Question

I'm asked if $\mathbb{Q}(t):\mathbb{Q}$ a normal field extension. I'm using the fact that an extension L:K is normal if and only if L is the splitting field for some polynomial $f\in K[t]$. I want to say that this extension is not normal, but am not entirely sure why.

Answer 1

Hint: is the splitting field for $f \in K[t]$ finite over $K$? Is $\Bbb{Q}(x)$ finite over $\Bbb{Q}$?