Is it normal to use glue to fit carpet?

I need my stairs carpeted, there's a set of 3 corners steps and the rest are straight. Each step has a bullnose and I want the carpet to wrap around the bullnose and sit flat against the riser.

I was told by a carpet fitter today that this will cost £150 to fit with wrap around and they'll need to glue the carpet against the riser and nail the carpet under the bullnose on each step with grippers on each step.

The nailing bit I get, although I thought it would be staples but glue was the first I've heard of this but I'm not a carpet fitter! Anybody here heard of that before?

Alternatively, they would fit the carpet straight (without wrapping it around the bullnose) for £80.