Hmmm not sure on that. But I read that the length of roots is fert related. If there's plenty of nutrients in the tank the roots stay short. If the tank doesn't have many nutrients, the frogbit will grow long roots to look for those nutrients.
AquaticBrandon is correct about the roots growing longer when they are "looking" for nutrients. It's not an issue though, as you can trI'm the roots easily with no issues. Just trI'm them to 1-2 inches long, and you are good to go. They will grow back and then trI'm again as needed.
Also, frogbit does well in just about any tank. One thing that it doesn't do well with, is a lot of surface movement. It prefers to settle in a still corner. You can use some airline tubing or even fishing line to corral it into a corner if needed.