I edited this post from asking how to solve the issues of acquiring Boolean Gemini to helping give people the solution to this issue.
First, you need to finish the quest that has you kill 2 Taken Zealots on each planet.
Then after turning it in, you may have to wait a few hours up to the daily reset before Petra gives you the quest 'Lost and Found,' and definitely take that quest.
Finnally, it seems that Boolean Gemini isn't guaranteed to drop after 'Lost and Found,' but it still could, so it seems like the gun is awarded randomly from one of the Reef quests like 'Lost and Found,' 'Wolves of Mars,' etc.
If you're still having trouble with this you may need to have your Queen rank at 3 or above, but I'm not sure if this is nessisary. Let me know if you got it under rank 3 with the Queen.
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6 RepliesWhy would they do this level 3 B.S.? If that is true then the quest shouldn't have even unlocked until I hit lvl 3. Now I feel like I wasted a ton of time that I could have been putting into a different quest and gotten a reward that could be beneficial to me now. Not months from now because that's how long it's going to take to lvl up Petra with 3 bounties per reset. To everyone saying that I neglected her prior to the taken king.... I just started this game on ps4 on Tuesday so I had no way of getting anymore rank than what I have now which is around 1-3/4. I did this quest because I figured having a strong primary would help me the most right now only to have her give me absolutely nothing. They should make a way to rank her either with daily bounties or a class item that gives rep. I believe this was unintended on their part BTW at least I hope it was.