I have used white vinegar.
Lots and lots of salt will kill anything eventually
Hi Mar: I don't know about this killing the roots too, but you can try it.
Homemade Weed Killer:
I've heard this works. Don't know if it will kill the flowers, though:(
1 gallon of Vinegar
2 cups epsom salt
1/4 cup of the original BLUE Dawn dish soap
Mix in a spayer.
It should kill anything you spray it on. Mix and spray in the morning and after the dew has evaporated. This solution works best if you use it on a hot day. By evening, the weeds should be all gone.