Answer: A non-selective herbicide will kill burdock. Glyphosate, sold commercially under the name Roundup (among others), is an example of a non-selective herbicide. Glyphosate is considered by many authorities to be more "environmentally friendly" than alternative products. With this and with any herbicide, follow the label instructions and cautions exactly. Glyphosate will kill most plants within a few days, generally breaks down within two weeks after application, and does not tend to migrate into the soil.
Since Glyphosate will kill or damage any plant whose leaves or green stems it contacts, here's a way to eliminate deep-rooted, established perennial weeds that have come up in the middle of a bed and can't be sprayed: cut the stem and apply a single drop or two of undiluted Glyphosate. This will kill even persistent thistle, burdock, and pokeweed, is economical, and doesn't endanger surrounding plants. Wear protective gloves during this process and wash up thoroughly!
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