If I were to rent a bedroom in my house would I need a formal rental agreement? And would there be a problem of just throwing them out if it did not work?

I'd definitely have an attorney draft up a formal rental agreement. And "just throwing them out" does have its problems. It actually entails eviction proceedings, which like any other legal process is typically long and drawn-out and can only be dome if they subsequently violate the agreement, which is why it's important to have everything in writing. Just "not working" isn't grounds for eviction. If you're so doubtful that you even have to ask this question, that may be your best indicator of what to do (or not) right there.

1. First unless it is zoned properly this may be considered an illegal rental.
For those that rent illegal apartments, the renter can actually latter sue for all of their rent back. So be careful.

2. always have a rental agreement, and you can never just throw them out, you will have to evict them.

Can a rental agreement be done when renting a bedroom by the homeowner?