We used to have a Norway maple in our front yard, and that tree would send roots all over the lot, out to at least twice the diameter of the tree. As a result, it was difficult to do any gardening within 30 feet of this tree. I don't know the source of your roots, but there are other plants that send out lateral roots. These roots will compete with your garden plants for moisture, so they really have to go if you want the garden to succeed. Once you have dug out the roots, and prepared the bed for planting, there is only one way that I know of the keep the roots from returning. You would have to sink some sort of barrier, typically steel or concrete, around the bed, at least 10 inches deep. 16 inches would be better.

Presumably if there are roots and they belong to this 'flowering plant', the plant is growing somewhere nearby or in the bed itself? Kill it and your troubles are over.

Or, if you want to keep some of it, confine it to an area and put down a sunken barrier as ericwi suggests.

Are you sure they're not tree roots?

I have the same issue with my vegetable garden, on one side I have an enormous lilac bush 15 feet away from the bed, on the other side fruit trees 15 feet away from a bed. When I planted them 17 years ago, they were twigs, and 15 feet looked like plenty of distance. Now, not so much.

When you add all those good soil amendments, the invasive roots just love it and grow back pretty quickly. I use a pick to tear them up, going down 6 inches or so, then I don't bother to remove the small root bits, just plant in amongst them.

What I've found is that the invasive roots suck up the moisture very quickly - IOW there are plenty of nutrients, the veggies I plant will grow just fine if I water them more frequently, like every 2 -3 days, instead of once a week that works for the rest of the garden.

The roots are from Japanese anemone btw.

I battle roots too. They suck the moisture out of soil and it is really hard to grow anything within many feet of the tree. I wonder about the authors who talk about "understory" plants. How do they compete with the tree roots? I end up watering the top couple of inches in order to have something colourful underneath the trees. However, it is not an option to remove the trees, so I try to cope.

Thanks for the avice. I took out what root clumps i could, added 2 3 cu foot bags of soil, pl;us organic miracle grow fertilizer then just planted the vinca and impatiens. We shall see how they do.