More precisely, it's why Roth felt comfortable with having the Rosato brothers pretend to ALMOST kill Pentangeli.

Michael wasn't even supposed to know Roth was backing the Rosato brothers. Michael simply mentioned that he would kill Pentangeli as a (supposed) courtesy to Roth so he would know what was going on in New York when the Rosatos would gain more power and be a stronger force after Pentangeli's death.

How Roth had set things up, Michael would think Pentangeli wanted Michael to "take off the cuffs".
With Michael supporting the Rosato's claim to those three territories Clemenza had promised them, ordering Pentangeli to give those territories up to the Rosatos (and as a consequence, weakening Pentangeli) Michael could be fooled into believing that Pentangeli was protecting his own interests in New York.

Michael knew better. Roth did not. Roth MIGHT have known better had Fredo told Ola that Pentangeli's meeting with the Rosatos was to hand over those three territories and make the peace per Michael's order.

In the end, Roth did the only thing he could- get Pentangeli out of the way and hopefully make him a pawn to turn against Michael.