  Let $\mathbb{Z}_p[x]$ be the set of all functions whose coefficients are in
the field of $p$-adic integers $\mathbb{Z}_p$. This work considers a problem of
finding a root of a polynomial equation $P(x)=0$ where
$P(x)\in\mathbb{Z}_p[x]$. The solution is approached through an analogue of
Olver's method for finding roots of polynomial equations $P(x)=0$ in
$\mathbb{Z}_p$.
