If it's a very general term, you can expect a lower quality score. I would break out all the queries it's being matched to as exact matches, effectively using the broad match to research keywords.
You can find more info here: http://www.rimmkaufman.com/rkgblog/2010/09/28/negative-keywo...
Do you maintain "scent" from keyword to ad copy for this keyword? http://www.grokdotcom.com/topics/senseofscent.htm
If scent is not maintained you are hurting your clickthrough rate which accounts for a majority of the weighting behind quality score.
I didn't mean to imply that changing the match type will magically increase quality score. To me breaking them out as exact matches is about making the targeting better, both for the text ad and the landing page, which sets you up for a better quality score.
I'm fond of the "keyword trap" approach as described here http://www.clickequations.com/blog/2008/12/the-match-type-se..., but the same thing can be accomplished in one ad group with multiple match types if bid correctly.
Is this helpful matthewcford?