You won't be able to repair that and not see where it was broken without using some kind of paint. Applying glue or cement works, but if the surface isn't prepared properly, it can peel off because it won't bond with the plastic, which is one reason a solvent-based cement is needed and it will need to be reinforced by something that can bond with the plastic.
I would look on ebay for a replacement- not everyone wants to keep the base for their TV and when someone finds that they need one, ebay is a good source.