How do I get rid of plants with tubular roots (other than weed killer)

was given violet looking plants to put around flower bed several years ago. Have tried digging up and they have tubular roots. Now are spreading in grass, and weed killer not doing anything to get rid of them taking over.
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Wherever they pop up, dig them out. May take several seasons before you get all of them.
People need to research what they plant in their yards...... invasive plants are wrecking many environments. Dump straight vinegar mixed with salt(alot-1gal. vinegar/1cup salt) on them it has to soak into ground to get to tubers,this kills everything . Or use a glysophate herbicide. or The only other way to kill violets is to dig them out, making sure you get all of the tuberous roots.or they spread even more.
Since they are all over your yard and that many can't be dug up, you'll have to kill the entire yard or treat with an herbicide.