Unfriendly Persuasion

 is a quest in Fallout: New Vegas.

Quick walkthrough
Marcus asks you to convince some NCR mercenaries to go away peacefully. With 65 speech you can simply ask them to leave and complete the quest. If you are Idolized with the NCR you will have an option to use your NCR reputation to convince them to leave.

If you ask them how much it costs to bribe them they will say 2500caps. You can get the caps from Marcus by asking him. If you then use speech to convince them to leave for free you have just earned a mint. Finally you can just kill them all, this is actually pretty easy considering that they all never move and can easilly be taken out with a silenced scoped weapon from afar for a sneak attack critical. To make it even easier Marcus and a random mutant will come to your aid! In fact they even have enough health to kill them all for you. The downside of course is NCR infamy.

Detailed walkthrough
First after finding Jacobstown Marcus will approach you with news of New California Republic mercenaries harassing the town. He'll then ask you to peacefully deal with them. When asked why the the mutants don't kill them Marcus says it's to avoid the NCR from having an excuse to terminate Jacobstown.

Finding the mercenaries is relatively easy in that they're directly in front of the town. To resolve the quest you can give them 2500 caps or with a 65 Speech test peacefully tell them to leave. If you have very high NCR standing you may also be able to tell them that you're an NCR hero, and they'll leave without a speech check or paying them.

A way to get caps, Loot and no Infamy is to go to Norton (mercenary leader), ask him how much it would costs, go back to Marcus and  to him for Bad Karma and get the 3,000 Caps. Then get in a hidden position (behind them) and take every mercenary out with a Silenced Sniper Rifle, then go to Norton and either convince him to leave (65 Speech), or pay him 2,500 caps. Then back to Marcus, and tell him you solved it "peacefully".

Note: as of 10/25, you will get an Infamy hit if you try killing the mercenaries after getting caps from Marcus but before completing the quest.

You won't get any Infamy hit (bug? you do get a hit if you kill them after the quest is completed), and you will get their loot (2x Plasma Rifles, 2x Sniper Rifles, Heavy armor, and associated ammo). And if you have don't have enough Speech points, you still get 500 caps (versus the whole 3,000 caps). Only drawback would be the Karma hit from lying to Marcus, and you don't get Norton's loot (Assault Rifle, armor, and a note describing his mission).

If you have no Speech or no powerful silenced weapon and really want Norton's loot you can kill them all, but Marcus won't be as happy. There's 4 ways to kill them all.

1. Use a long range suppressed weapon and mines to take them out with sneak attack criticals and explosions (Or just a Silenced Sniper Rifle, head-shot sneak critical will kill them).

2. Take them out head on, Anti-materiel rifle with Armor Piercing rounds recommended.(hardest)

3. Attack them then run to Marcus (make sure he doesn't die, but he has 500HP and 30DT) and the other Super mutant and let them kill the mercenaries. (easiest)

4. Shoot them one after another (headshots or other one-hit-kills) from a position where only the person you're currently killing would be able to see you. It doesn't even have to be a silenced (or scoped, if your manual aim is good enough) weapon; the others will become hostile for a short while, then turn back to friendly/neutral.

After completing the quest you get 350 XP.