A, I believe because they both have the same root word
Because it will help prevent the sickness from forming or worsening into a more deadly form
This shows how much Claudius cares about being King and holding onto his throne.
He knows that the public loves Hamlet, which is why he can't just arrest him for the murder of Polonius, he has to be much sneakier and trickier than that, otherwise the public will take Hamlet's side and Claudius will lose support.
