Gertrude implies in her opening words to Rosencrantz and Guildenstern that the she and Claudius have invited the pair to Denmark for Hamlet's benefit. Although Claudius may have ulterior motives, Gertrude is the person who insisted on contacting Rosencrantz and Guildenstern and bringing them to court because of the friendship and respect that Hamlet bears for them. At this point in the play, one can reasonably assume that both Claudius and Gertrude had Hamlet's welfare in mind when they summoned the two Germans to court.
Claudius, however, is once again aware that all eyes are on him as he solicitously welcomes Rosencrantz and Guildenstern and expresses his grave concern for "Hamlet's transformation." Although Shakespeare gives no suggestion that Claudius had anything but Hamlet's welfare in mind when he summoned Rosencrantz and Guildenstern to court, the reader knows that Claudius does nothing without self-promotion in mind. His suggestion that they report back any affliction of Hamlet's echoes Polonius' instructions to Reynaldo in Scene 1 regarding Laertes. Both Polonius and Claudius exhibit distrust and deception when dealing with their heirs. When Rosencrantz and Guildenstern heartily agree to do the King's and Queen's bidding, Gertrude promises they will receive "such thanks / As fits a king's remembrance." Claudius has successfully deceived Gertrude as well, convincing her that he loves Prince Hamlet.
When Polonius ushers in Cornelius and Voltemand — Claudius' ambassadors to Norway — the old man entices the King with a promise that he knows something about the Lord Hamlet that Gertrude and Claudius cannot know. He refuses to divulge any information until after the ambassadors have left, but he creates excitement over his "find." Gertrude, motivated only by her deep, even overprotective, love for her son, remains skeptical about Polonius' ability to help.
