Any question may have positive and negative answers (in reality).
This is an example:
How do I do [this]?
When this happens, I have no choice but to accept that answer.
It is annoying when someone else sees the question and accesses it to see the answer, and leaves disappointed.
So, to fix this you can add a button to mark an answer as a negative one.
An impossible question should have a different color on the answer and probably a page prefix so others (including from search engines) don't waste their time looking further.
A real example is this question of mine.
Edit: I see that the advantages are not so obvious:
It saves bandwidth for both the server and the client and might save seconds to minutes of the reader's time.