They should be good for a few days. You can do an online search and should be able to find out for sure. I love roasted beets with blue cheese, balsamic vinegar, shallots and cracked black pepper on salads - yum!!
If you're keeping the beetroot in an airtight container in the fridge, it'll be fine for at least a week, and though I usually use it all within the week, it may keep even longer. You can also chop them up and freeze them and they'll keep for several months...it's perfect to puree or to make soup.
Mmmm. I did the same thing today. I expect the beets to keep til Friday or so, but we'll probably finish them before that.
A local restaurant here makes a fabulous salad of sliced beets on arugula, with slivers of parmesan cheese on top, cracked pepper and a light viniagrette. We're having that Tuesday night with roast chicken. Yum.