One recent question was asking if a quote is authentic:
Did Gandhi say "The most violent weapon on earth is the table fork"?
If I could find a reference for this quote then life is perfect.
But in this case, I couldn't find any recorded evidence that Gandhi ever said that quote, it isn't attributed to him by any book or notable websites like Wikiquote, of Brainyquote.
Should I leave unanswered?
Try to find what that quote is based on.
For example, here and here and here I found they were misquotes for which I found original/actual quotes.
Gandhi could be difficult e.g. whatever he said might not literally have included the word "fork". Gandhi needn't have been writing in English, and many of these internet sound-bytes are a paraphrase/summary of what was actually said.
If you can't find evidence for the quote it would be interesting (evidence) to find a related quote of what he actually said. Did he ever say anything like it? Was it in the context of a political weapon against the British? Did he ever have anything to say about vegetarianism and animal welfare? That would at least let you answer with "plausible" or "implausible" (which is better than nothing), and leave readers a bit better informed about what he actually said.
This will help: FAQ: What constitutes original research?
Negative searches
Answers are original research when they are based on the fact that the answerer found no relevant results when looking at non-verifiable or non-replicable search results, such as Google queries.
How to fix
When you want to link to a search, typically to "prove a negative":
Use a tool which allows reasonably good replication of the results. For example, Google is known to provide different answers per user, so it's not acceptable.
Use a reputable tool which has an extensive index.
Document your search terms.
Note that you will not be proving a negative so make sure your answer does not jump to unreasonable conclusions. At best, a negative search can support a "probably not" or, more likely, a "unknown" answer.
An alternative approach is to cite a relevant expert in the field, who has reported that they have searched for evidence and found none. This suffers from the Argument from Authority fallacy, and is merely likely to be correct, rather than definitively correct. Despite that, it is sometimes the best we can do to demonstrate a claim has no substance behind it. Once again, care should be taken about the conclusions drawn from such an argument.
