Let $R$ be a henselian ring. Is $R[[x]]$ also a henselian ring?
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Yes, it is. More generally, the following result holds.
See N. Sankharan, A Theorem on Henselian Rings, Canad. Math. Bull. 11 275277 (1968), in particular Corollary 2. Remark. The Proposition above is no longer valid if one takes the polynomial ring instead of the power series ring. For instance, if $K$ is a field than $K$ is henselian but $K[x]$ is not. 

