Suppose that we have a field $K = \mathbb{Z}_p(t)$ where $p$ is prime. (So this is the field of rational polynomials with $t$ as the variable)
Let $f = x^p - t$ be a polynomial in $K[x]$.
How can one describe the roots of $f$? I stumbled across this example but I was just wondering how the roots would look like.
An obvious root of $f$ is $\sqrt[p]t$, but what are the other distinct roots of $f$?