Dig holes at the base of the King Palm using a small shovel to expose the roots of the tree. The King Palm has a shallow root system, so you shouldn’t have to dig too deep.
Apply herbicide to the roots of the palm tree. There are several herbicides that will effectively kill the tree roots on a King Palm, including Epson salts, oryzalin, and trifluralin. Even fertilizer can be poisonous when applied directly to the root system.
Cover the base of the King Palm with a tarp for at least two weeks. The combination of herbicide and lack of direct sunlight will damage the root system.