Answer: The tree roots are invading the planted area because of the moisture and nutrients you provide to your annuals. A permanent fix would be to put an above-ground planter there and line it with black plastic before filling it with potting soil. This will exclude the tree roots. Hosta roots are fibrous and generally matted together (have you ever tried to dig and divide a hosta??), and the tree roots cannot penetrate the mass. Therefore, the hosta, by virtue of its tough root system, is able to grow well, even with competition from the tree roots. The roots of impatiens are fine, tender, and easily defeated. You might try planting your impatiens in plastic pots and sinking the pots into the soil, so they'll have their own root space. Or grow plants with tough, intertwining root systems, like Astilbe. It really is difficult to grow annuals under trees!
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