Preheat the oven to 200 degrees C. Put the prepared swedes, carrots, parsnips and turnips into a large saucepan. Sprinkle with salt and pour over enough boiling water to cover the vegetables completely. Bring them back to the boil and cook for 5 minutes.
Drain the vegetables thoroughly through a large colander. Put the dripping or olive oil into a large roasting pan and heat in the oven for 10 minutes. Take the pan out of the oven and carefully add the drained vegetables to the hot fat. Sprinkle with the herbs and baste well until the vegetables are evenly coated. Roast, turning once, in the centre of the oven for 40–45 minutes, or until tender and browned. Serve hot.