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Field bindweed is one of the worst weeds to try to eradicate because it has an extensive root system. In fact, the roots can grow down more than ten feet. If it is cut or dug, the remaining rhizomes in the ground will send up new shoots. In addition, bindweed seeds can remain viable for up to fifty years. It is considered one of the ten worst weeds.
Here is a link which discusses some means of control. I hope it helps you.