I dont think it will be that easy to kill with access to just one root. I am sure it has sent roots in all directions. I am no expert but it would take months of poison dosing to kill such a huge tree, and I dont even know which poison to use.Poisoning it is a terrible idea. You have no idea which tree it comes from, and if you kill the tree you could have very angry neighbours on your hands.
The garlon 4 suggested is actually a growth hormone which causes abrupt cancer like growth in the tree which kills it. From what I read it works quickly on small shrubs and big trees that have been cut, not a fully alive big tree.