What message do Rosenerantz and Guildenstern carry to the king, and what is his response?

Rosencrantz and Guildenstern were summoned by the King and
Queen to find out why Hamlet is not acting like himself -- why "the exterior not the
inward man / resembles that it was."  They want to know if it is more than his father's
death that has brought about this change.  The King specifically suggests that they
"draw him on to pleasures, and to gather / so much as from occasion you may
glean."

Rosencrantz and Guildenstern do the best they can
to discover what is going on with Hamlet, but very quickly, Hamlet becomes suspicious of
their motives and asks them directly, "were you sent for or no."  When the two don't
respond directly, he dismisses their friendship.

In a
wonderful play of irony, they tell Hamlet that they passed a troupe of actors on their
way to Elsinore.  Hamlet decides to have these actors perform a play that he has changed
to mirror how Claudius killed King Hamlet. He hopes that King Claudius will reveal his
guilt.

When Rosenerantz and Guildenstern take the message
to Claudius about the play, Claudius seems pleased and
says,

with
all my heart, and it doth much content me

to hear him so
inclined.

Good gentlemen, give him a further
edge

And drive his purposes on to these
delights.

Claudius doesn't
realize that if the play goes as Hamlet hopes, Claudius will be
doomed.