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Usually a supplemental result indicates a page that google has found (somehow) but the link to the page is no longer valid. For example the linking page may have been deleted or only temporary, or in one case I have seen the number of links on the linking page was far too many (1000s) for Google to follow.
Usually these supplemental results disappear from SERPS, so I would suggest trying to get Google to revisit your site. If you have access to them, check your logs to see if Google is visiting.
Another simple check is to see if the page has any PR in the Google toolbar