I have one or two perennials that spread via underground roots and are very invasive. Although I've dug them up is there anyway of killing the roots under the soil to stop them regrowing? Thanks.
Other than digging them out every time you see a new shoot, the only way I know is to put systemic weedkiller such as glyphosate on the plants as this gets taken down to the roots and kills them. It is best done when the plants are in active growth. You would need to protect the plants you wish to keep.
Constant lookout for the emerging plant and pulling/digging it up as deeply as possible straight away may not entirely solve the problem but it does weaken the plant(s) and makes the gaps in between 'treatment' longer. I am having the same problem with Japanese anemone - can anyone tell me why Alan Titchmarsh and his ilk still recommend this plant? Pretty as it is in full bloom, it's still a thug!
Do you want to get rid of them entirely or would you be happy to have some left? If you would like to keep some in the flower beds, dig the lot up and clean the bed as much as possible, then bury a length of some DPC blackplastic strip in a circle and plant a bit of the root in the circle. Generally speaking, the plant will then stay within the confines of the strip.