If it is american frogbit and not Amazon frogbit, then this is natural for the plant. As a pond plant, its roots will reach all the way to the pond bottom in water that is a foot deep. I have never seen duckweed with roots more than a couple inches long at the most, usually half that.American frogbit both have extremely long roots.
Adding an extra pinch of fish food that the fish won't eat will raise nitrogen levels, but you want to be very careful doing this.
You may want to go with Amazon frogbit instead, which is a smaller plant more suitable for the aquarium and has shallow roots