I find, Michael's visits and the sequence of events somewhat bizarre....

Michael didn't seem to suspect / see through Roth as to why Roth in Miami with no business interests of his own in New York was backing up the Rosato brothers in New York against Pentangeli, Michael's [and Vito's] own loyal, good old man for years until the Tahoe bedroom shooting. Ahhh.... Roth fooled a Corleone but Pentangeli was smarter

  • Michael didn't question -- And what is the interest for Roth, in concocting this Love Triangle?!
  • did Roth gamble? on Michael's [the heir-apparent] greed for Roth's business that Michael would “give his loyalty to a Jew before his own blood” Roth was not wrong!

Whilst my take, Michael's “Then Pentangeli is a dead man, you don't object.” was a statement rather than a question and Michael was telling [not asking] Roth what Michael was going to be doing ie: Michael was not seeking Roth's approval nor permission
Quote
I came here because there is gonna be more blood shed.
I want you to know about it before it happens so that there's no danger of starting another war.

  • why did Michael need to visit Roth at all -- because of....
    The important thing? is that nothing interferes with our [Roth and Michael's] plans for the future.
  • what is the link between Roth and Michael's plans and the Tahoe shooting
  • Roth's been flying under the Radar
    Quote
    Hyman Roth always makes money for his partners.
    One by one, our old friends are gone. Death -- natural or not - prison -- deported.
    Hyman Roth is the only one left -- because he always made money for his partners.
  • starting another war by whom
  • Roth has never shed any blood never started war/s
  • why would the Mighty, Top Don Michael Corleone, visit his subordinate who, according to the Don himself, had just “tried to have Michael killed” In my home! In my bedroom!
  • If Pentangeli is small potatoes, how could Pentangeli have engineered such a hit of the Top Don In my home! In my bedroom!
  • Did Pentangeli come prepared anticipating Michael's no “to get rid of the Rosato brothers”

After the failed Tahoe shooting and Michael's visit to Roth
1. Neither Michael nor Roth fooled the other
2. Neither was relaxed and confident, in their friendship
3. Both conspiring to get the other killed -- First
4. Both knew the other knew but continued their charade until the First dead man
5. Both underestimated each other, more so

Quote
Roth: What we'll do together in the next few months will make history, Michael -- history
Michael dispatching dead man, Pentangeli on a peace mission with the Rosatos, would make Roth think? his relationship with Michael is still good, he’ll be “relaxed.”

Sure thing Tuna sandwich Picnic!