The version given above - that is, "This answer is not negative either" - sounds best to me.

You can translate it using "neither" but the word order needs to be a little different. It would be, "Neither is this answer negative." If you want to use that kind of structure, then "Nor is this answer negative" sounds better to me, although gramatically I don't think there's a difference.

Here's a pretty good page with examples of "neither" and "nor" usage: http://dictionary.cambridge.org/us/grammar/british-grammar/neither-neither-nor-and-not-either

This kind of sentence would be what that page describes as, "We use neither and nor + auxiliary/modal verb + subject to mean ‘also not’. "

Would work for "Neither is this answer negative" - assuming it followed a sentence about another answer that was not negative.