This is already available for the Forums.  Click the 'Unanswered' tab at the top.

But that only returns all the unanswered posts no distinction. 

It would be useful to select an option on the search to return all results on the search i submitted.

Maybe I'm missing something.  The primary reason for searching in the community is to find answers, IMHO, so looking for posts with no answers is very counter-intuitive.  Can you describe how this type of selection would be useful? 

So its more a search to your own posts?