Finding number of roots of a polynomial in p-adic integers $\mathbb{Z}_{p}$ The problem is to find the number roots of $x^3+25x^2+x-9 $ in $\mathbb{Z}_{p}$ for p=2,3,5,7.
I read this equivalent to having a root mod $p^{k}~\forall k\geq 1$.
By Newton's lemma I can get whether there is at least one root.
Any suggestions on how to find the number of roots?

1)Using Newton's polygon method
2)Hensel's lemma
