Category-specific Archive Pages

I’ve been searching around but can’t find anything quite what I’m looking for. Running only one installation of WordPress I hoped to achieve the following:

I have two categories, we’ll say “root1” and “root2” and those are the parents of all other categories containing posts. I want the front page to display only things in “root1” as if that’s all there was, and then I want another page to act the same as the main page only displaying things in “root2” instead of “root1”. The side panel displaying categories could change or remain the same, either one is fine.

Is this possible? If so, how would I do it?