Fallout 3

Have you talked to people (other than bannon), about the council yet? I remember someone talking about seagrave wanting the spot on council and that was question that gave quest. like "so i hear seagrave wants your job" (not exactly but that was the gist of it)

There are some things you might've missed:
-I thought the same thing, but all I did was hack Seagrave's computer. But to really incriminate him, there's a note near his bed from Eulogy Jones (the slaver leader)
-If you talk to Bannon about the letter, he'll tell you to bring it to Commander Danvers. Perhaps you missed this.

You have to go talk to Chief Danvers. She is usually up stairs in the bunks. After you do that, THEN go talk to Bannon.

You have to have the note from Eulogy Jones about Seagrave being involved with him. After getting that, talk to either Bannon or Danvers, could be Harkness I believe if you didn't finished the replicated man yet. If you talk to Bannon he goes to Danvers himself, but you still get the Schematic, or if you talk to Danvers first go to talk to Bannon and a dialogue option will arise where you'll inform Bannon Seagrave is no longer a problem then you'll receive the Schematic, also note this a Free Form Quest, as it will not show up in the Pip-Boy quest menu, but one you just have to complete through dialogue.

You have to ask bannon "so you're on the city council" and he'll tell you that segrave is trying to replace him on the council and he'll ask you to find an incriminating letter in his room and he'd "appreciated" it then you find the letter under segrave's bed and you have to tell danvers about it and yo can either tell her that bannon is trying to blackmail segrave or you can give her the letter, if you tell her that bannon is trying to black mail segrave you'll get a discount from segrave and vis versa

You must talk to Danvers first then you can go to bannon to start the quest