During a discussion I had with @jgn based on the question discussing rolling twice on an investigation check, I realized we were operating with entirely different ideas of how dice rolls actually function inside of the narrative of the game.
A fighter searches a room he's never been in before. If he rolls a 15, he'll find the hidden switch that opens the secret laboratory of the mad doctor Fred. He rolls and it's a 3, he does not find the secret switch.
My point of view is that the fighter did his best to find something special about the room, didn't find anything, and has no reason to roll again, and he'd get a new try, or find it automatically, if somebody later informed him about the hidden switch in the room.
@jgn's point of view is that the fighter is aware of the fact that he did a poor job searching the room and can keep trying until he is confident that he did a good job. In essence, the fighter "knows" the dice roll and will stop trying when he rolls high enough.
To me, the later approach seems like it'd be better served with a taking 10 (passive) Investigation check and refluffing "Oh I rolled a 1, I did a poor job searching, I'll just roll again!" is essentially fishing for advantage based on meta game information.
In earlier editions, "try until you are 100% certain you gave it your best" was done with taking 20, but that no longer exists in 5e.
So which, exactly, is the official D&D 5e stance?
Notes based on comments:
There is, obviously, a risk of failure. The fighter can fail to find the room, so he should roll.
It is not critical that the fighter finds the room. This is not a case of "the fighter has to find the room".
Do characters know they did a poor job because of low dice rolls if a failed roll gives them no new information and their failure isn't visible?