If you are only putting in a single pipe, then either jmduke7 or lush96 are offering good advice. Additionally, since it sounds like your dealing with a mature tree, it might not be as much of an issue.
Now in my case, I was trenching near a tree where in a few years the trench WILL be within the drip line of the tree. I was placing multiple pipes in a trench, and my fear was tree roots growing between pipes and swelling in size of the years and break the pipe. So to help avoid roots growing BETWEEN pipes, I lined the side of the trench with vinyl siding.
And the other thing I would think would help... the deeper the better (the roots closer to the drip line will be closer to the surface, so the farther UNDER them you are, the less likely they will bother your pipes).