We say a polynomial $P \in \mathbb{K}[X]$ is seperable (where $\mathbb{K}$ is a field) if and only if $P$ has only simple roots in the algebraic closure of $K$.
We say an element $x$ is seperable if it's minimal polynomial is separable.
I'm currently searching for non-separable elements (preferable in $\mathbb{Q}, \mathbb{R}, \mathbb{C}$), but cannot seem to find any.
Best Answer
You can't find non-separable elements in $\mathbb Q, \mathbb R$ or $ \mathbb C$ because these are all fields of characteristic zero.
You should instead think about infinite fields of characteristic $p$. For example, consider the field extension $\mathbf F_p (t): \mathbf F_p(t^p)$, and consider the element $t \in \mathbf F_p(t)$. Its minimal polynomial over $\mathbf F_p(t^p)$ is $X^p - t^p = (X - t)^p$.