You would need to get it authenticated by a real Beatles autograph expert.
I'm not saying it is the case with yours, but anyone can create a fake letter of authenticity. I just Googled for "Rock This Way Memorabilia" and found nothing, so your certificate of authenticity isn't worth a great deal, unfortunately. There are many, many fake signatures out there, but if you believe the autographs to be genuine then it is worth investing a little bit of cash to get proper authentication done.
If you are looking to sell the record then offer it to someone like Frank Caiazzo who is a Beatles autograph expert - if it's genuine he may be interested. Or there are firms such as Tracks in the UK and Fab4Collectibles in the US which buy signed items. Personally, if I was looking to buy Beatle autographs I would only ever buy through one of those sources or via a well-known memorabilia auction house like Cooper-Owen. So if you are looking to sell then consider going via one of these routes - they will buy the record from you and resell it, but they will give you a fair price.
If you want to keep the record yourself but require authentication then get in touch with an autograph expert. I just did a quick Google search and came up with these sites - http://www.rogerepperson.com/
- as examples. There will certainly be others if you look on Google. Frank Caiazzo used to do authentication but has stopped now, I believe.
Good luck, and let us know how you get on!