Answer: I'll bet what you are finding are feeder roots from nearby trees. There's not much you can do to eradicate the roots without harming the trees. The roots are invading your flower bed because the soil is rich and moist. You may be able to sink a barrier around your flower bed to discourage the roots, but that would entail digging a deep trench and either pouring cement or setting something like a sheet of galvanized metal (such as is used for patio roofing) sideways in the trench. Wish I had more options to share with you!
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