After scaring Pentangeli with his shouting account of the Tahoe shooting, Michael tells Frankie that he .knows Roth was behind it, and asks him to “help me take my revenge.” “Michael, anything…” says the much-relieved Pentangeli. Michael then tells him to “settle these problems with the Rosato brothers.” When Frankie objects, Michael gives him the “keep friends close/enemies closer” rap, then explains that if Roth thinks his relationship with Michael is still good, he’ll be “relaxed…then I’ll find out who the traitor is in my family.”
All good, except that the last thing Michael said to Roth in Miami before leaving to visit Pentangeli was: “Frank Pentangeli is a dead man…you don’t object?” But, instead of having Frankie whacked, Michael dispatched him on a peace mission with the Rosatos. That would have told Roth that Michael didn’t suspect Pentangeli in the Tahoe shooting—meaning that he might suspect Roth. It would make Roth feel anything but “relaxed.”
Why did Michael send Pentangeli on that mission?