George,
The depth and extent of any tree's root system will depend on many factors, including soil type and density, soil moisture, irrigation practices, obstruction, etc, etc, etc. In general, roots will grow wherever soil structure, moisture, aeration, nutrition and temperature are favorable. Most roots do not grow more than 3 feet deep, with the majority in the first foot or so. Roots can extend one hundred feet or more from a large tree. Typically, I would guess the roots of your poplar tree extend about fifty feet or so from the trunk, but they will continue to grow as the tree gets larger. There is a very good chance that the roots will invade your septic system.
POSSIBLE TREATMENT:
The town of Ridgewood, NJ has been using this treatment since 1937. "One liter(1 qt) of 6-mm (.25-in.) diameter [copper sulfate] crystals are poured into porcelain toilet bowls. They are never poured in sinks, which have thin-walled traps. The toilet is flushed and the water in the bowl agitated with a plunger to make sure all crystals are carried down the drain. Semiannual treatments have controlled roots in tile sewer connections without discernable injury to the plants whose roots are killed." (Harris 1983).
Please be aware that I make no claims as to the effectiveness or safety of this method, I'm just passing along what I have read.
I hope this helps. Good luck.
Brett