Why did King Bradley allow the Elric brothers, Hughes, and Armstrong to continue investigating the military? In episode 10 of Full Metal Alchemist: Brotherhood, during the events in the Research Lab 5, Edward Elric is severely hurt. Later in the hospital, he writes down everything he had come to know, and he discusses with Alphonse, Hughes, and Armstrong about what to do with the information to continue the investigation.

At this point, King Bradley arrives with lemon into the room. He finds out what they are doing but acts very calm and chilled out and allows them to continue investigation while being careful.

Why did he not get Hughes and Armstrong killed at that point? Or at least tell them to not investigate at all?
This wouldn't work, for a number of reasons.
Ordering them not to investigate
If Bradley orders them to stop their investigation without cause, it could only mean two things:

Bradley doesn't want them to discover something, implying he is somehow involved with or related to their findings at the Fifth Laboratory.
Bradley is an idiot.

Since I don't think anyone present would accept the second explanation, it clearly implicates Bradley as being involved with the homunculi somehow. I doubt this would stop Mustang since he aims to become Fuhrer, and exposing the current one could help him achieve that goal. The Elric brothers would likely just be even more motivated as well.
Killing them
If Bradley killed them, it would indeed stop their investigation in its tracks, since everyone who knew about it would be dead. There might be some gossip about the Fuhrer inexplicably killing military officers, but it would probably quiet down eventually.
However,

He cannot kill Ed or Al since they are important sacrifices for the homunculi's plot to

 turn Amestris into a philosopher's stone.


He can't kill Mustang either since he's a potential candidate for the above plot.


He could kill Hughes and anyone else present, but that would just add fuel to the fire for Mustang and the Elric brothers, increasing the chances that they will discover his real motives.
For these reasons, he decided to allow them to continue their investigation in the hopes that they will be thrown off of the trail and not suspect that he is involved.