Let $K$ be any field with a non-Archimedean valuation $| \: |$ , and let $R= \{x \in K : |x| \leq 1 \}$.
Let $f(x)$ has discriminant $D$, and let $a_0 \in R$ satisfy $|f(a_0)| \leq |D|^2$. Show that $f(X)$ has a root $a \in R$.
Can see the similarity to Hensel's lemma, but not sure how to use it!