Keep in mind this is my opinion, I think your fine with that span, however if inspected it wouldn't pass code.
Here something I do regularly, we build a lot of decks that span 10ft to a beam on almost every deck we do. We use 2x10s, and I've yet to see and saging, keep in mind the only load we have are decking boards and whomever is on the deck at that time,
I don't know the load that is on your beam, that is to me the desiding factor whether this will be ok. If your nervous still about using that beam, just ask a structural engenineer and hell be able to tell you what you can use, most likely he'll have you use a microlamb beam.