You can definitely roast asparagus and potatoes together. When roasting asparagus and potatoes together, there are a few things to keep in mind. First potatoes take longer to roast. Second, roasting time for potatoes will depend on the size of pieces you are roasting. What I do is buy small red potatoes (petite sized) and either slice or quarter them, depending on how small they are. Lay them on half of the baking sheet first, drizzle with a small amount of olive oil, salt and pepper and roast them for about 8-10 minutes. Then, I add the asparagus to the baking sheet and roast the asparagus and potatoes together for ten minutes. If the asparagus spears are perfectly roasted but the potatoes are not, simply use tongs to carefully place the asparagus on a plate and return the potatoes to the oven to continue roasting. Check on them every three to five minutes until the edges are brown (not burnt) and the potatoes can easily be pierced with a fork.