Is it safe to go over roots at high speed on a cross-country bicyle?
It's safe as long as you use your body properly. Learn about:


proper neutral posture while descending:

light hands, heavy feet (stay above BB, mostly with your feet)
don't sit
knees bent
elbows out
back straight
look ahead (read the terrain), not on your front wheel, nor the obstacle itself for too much time

dealing with obstacles (roots, rocks etc):

choose a good line, since you are already looking ahead and not down
compress/weight before an obstacle
uncompress/unweight while hitting the obstacle



If you've never heard, thought or done any of the above before then give it a try. It'll improve your safety, confidence and handling on the bike. If you've been riding long enough not doing the above then it may be difficult to adjust. But it'll eventually happen. It needs practice and it'll not come overnight.

If you find this stuff interesting and you are really interested in improving your technique I suggest finding a skills lesson/course to take and also reading http://www.amazon.com/Mastering-Mountain-Bike-Skills-Edition-ebook/dp/B004D2BD1Q