True or False: Polynomial has non-trivial solution in $Q_p$ iff has non-trivial solution in $Z_p$?

Question

For polynomials, it is true that it has non-trivial solution in $Q_p$ iff it has non-trivial solution in $Z_p$? It seems to be true for homogenous polynomials, but seems not true for non-homogenous case.

For example, Suppose $x^2=2$ has $a=p^{-n}b$ where $b \in Z_p$ as solution in $Q_p$. Then it only shows $x^2=2p^{2n}$ has non-trivial solution in $Z_p$.