finite extension but not algebraic exetension

Question

I was reading about algebraic extensions. I want to know is there any example where finite extension of any field F is not algebraic extension.

Answer 1

Every finite extension is algebraic. If $L/K$ is finite, and $a \in L$ is given, then there is some $n \in \mathbb{N}$ such that $1, a, a^2, \dots, a^n$ is linearly dependent over $K$ and you get a polynomial over $K$ which has $a$ as a root.