When doing a search, if I come across a [closed] question, my head does try to ignore it and move to the next item in the results list. However, I often find that if I review those closed (duplicate) questions, useful information may be found in the internally linked duplicate.
The search results don't indicate why a question was closed, but if it was closed as a duplicate, it would be helpful to offer a link to the original question right there along side the closed question identified in the search results.
For example, this question links to another by the same person (and in this example, they appear next to each other in the results, but it's not always so obvious):
The only way to see that link and the reason for the closure is to open the link to the question.
I propose that the link see at the top of this page also be listed next to the main link like so:
The formatting/placement is not so critical; this is just an idea. Overall, it may be helpful to show this here, so that someone searching knows that there may be an answer for them in one of the two links, especially given that the tags of these two questions are quite different from the another.