I enjoy some totally fine roots contained by my flower bed, any hypothesis of how to carry rid of them minus riuning my soils??
Answers: Those are probably tree roots using the improved soils you hold created for your plants. As long as the beds to not cover ample areas under the drip-line of the tree (the outer reach of it's branches overhead, you can go around the edge of the bed and edge it next to a long sharp spade - cutting into the point or the turf and cutting a flash around the bed to stop the roots from using your planting beds - also cut out a small piece of the edge to create for a while mote around the bed - called an "air-gap edging" this reduced turf and root infiltration into the bed. With that done, the roots contained by the bed should break down over time. You can leave them contained by as compost, though, and keep your soil structure surrounded by the bed intact which makes the soil well again and more weed-free.
You can pull them out or use something such as RoundUp. RoundUp go through the leaves, down the stems, and into the roots to get rid of the complete plant. RoundUp dissipates when it touches soil.
RoundUp will kill any plant it touches. If you own flowers, "paint" RoundUp on the weeds you decision to get rid of.