I'm a fairly novice gardener and am trying to identify a plant that is
spreading and starting to take over a flower bed. I've searched the web
trying to identify it but have found anything yet. To my untrained eye its
leaves looks a bit like those of an ivy plant, but I could be way off the
mark there. Each leaf is a mixture of red, green and gold, and the stem is
also red. The leaves are not shiny. Above ground the stems grow upwards
rather than spreading, but the tallest shoot is only about 6 inches tall.
Underground however there is a huge mass of quite thick and very tough roots
which all the stems are connected to.

Does anyone know what it is?

I want rid of this plant before it takes over more of the bed and so far
have been trying to dig up all the roots. Is that the best approach?