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.
A reference is the paper by N. Sankharan A Theorem on Henselian Rings, Canad. Math. Bull. 11 (1968), 275277. See 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 The Proposition above is no longer valid if one takes the polynomial ring instead of the power series ring.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. 

