Carrots are a storage crop, and prefer a cool, dark, and moist place. They will get soft if they start to loose moisture; store either in a covered container in the fridge with a wet cloth, or even in a container of moist clean sand in a pantry space. Depending on your storage method, they can last anywhere from a couple weeks to a couple months.
The way we prefer to prepare carrots:
Recipes we like for scallions: