Let $p$ be an irreducible polynomial in $k[x]$, for some characteristic 0 field $k$. So we have a valuation $v_p$ corresponding to $p$. Now take $a$ to be a root of $p(x)$. Then $(x-a)$ is irreducible over $k(a)$, and $v_{x-a}$ is a place lying over $v_p$.
What is the degree of the extension $\kappa(v_{x-a}) / \kappa(v_p)$? (here $\kappa(-)$ denotes the residue field).