I've had carrots in a plastic bag in the fridge for a few weeks and when I went to use them today, I noticed there are what I can best describe as white bristles or whiskers coming out of them. I've never seen this before. What are they and have the carrots spoiled ?
They're just roots.
Don't forget that carrots are a taproot and this one seems to be trying to grow.
The carrots are still fine to eat, though they use the internal sugars to grow the roots, so they may not taste as sweet. They'll also get soft really quickly, so if you're going to eat them, do it soon.
Related question here.