How to get rid of roaches once and for all?

The only other thing I can think of is my carpet hasn’t had a good cleaning or been replaced since moving in. I have vacuumed once in a while, but I still don’t understand where these vermin are coming from.

I usually spray them with a couple shots of Fantastik, which seemed to kill them right away, but then later, they would just keep coming back. So I finally got out the Raid and sprayed along the edges of my kitchen and had success in killing one.

Are there any other ideas that I could use? I’ve also tried the toxic raid traps, but they haven’t done their job.

I live on the second floor.