Break them. Sinking and floating just tests the amount of gasses. Older eggs kept in low humidity will float even if they aren't technically bad. They may or may not taste the greatest but I've broken some very old eggs that were not rotten and had just evaporated all the whites. Some eggs kept in high humidity might be bad and not float.
Always break eggs in a seperate bowl from whatever your making or the other eggs in order to avoid a potentially bad one ruining the mix.