Answer: You're dealing with a formidable opponent! Tree roots can extend way beyond the canopy of the crown of a tree. Many trees trees are 'weedy' in that they develop an incredible network of surface feeder roots. These root seek moisture and nutrients and will out-compete the roots of annuals and perennials by virtue of their stronger drawing power. The roots gravitate to the soil of your flower beds because of the moisture that's available there. Outside of digging your beds, lining them with hardware cloth or tough weed barrier, replacing the soil and then planting your annuals and perennials, there's really no way of keeping the tree roots out. You may want to relocate your flower beds, or garden in raised beds (with hardware cloth attached to the bottoms of the beds) to keep the tree roots out.
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