I didn't even think about how we do roast veg here - peeled, cut up into reasonable chunks, tossed with olive oil (and maybe some roast veg seasoning - Masterfoods has one) and thrown raw into roasting pan with meat (+ some in another pan usually) for about 45 min, turning once usually around the 20 min mark.
Potato (white not sweet) takes longer than sweet potato, carrot, pumpkin or parsnip I've found - usually wants an extra 10-15min for me (or you could toss other veg in at about 15-20 min after potato and then turn them about 15-20 min later.)