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Here's the question, the card Unexpected Results says that you either play the top card for free if it is nonland or put it onto the field and return UR to your hand. My question is, what if the card is Sphinx's Revelation? Would the card get played with X=0 and no life and no cards are drawn?

Please autocard.
[c]Unexpected Results[/c] ⇒ Unexpected Results
Sphinx's Revelation

Creating a Rules Thread

X is undefined, so it's treated as zero.
You must choose zero for X.

107.3b If a player is casting a spell that has an {X} in its mana cost, the value of X isn’t defined by the text of that spell, and an effect lets that player cast that spell while paying neither its mana cost nor an alternative cost that includes X, then the only legal choice for X is 0. This doesn’t apply to effects that only reduce a cost, even if they reduce it to zero. See rule 601, “Casting Spells.”

Keep in mind that you're not required to cast the revealed card, so you could leave Sphinx's Revelation on top of your library.