My questions concerns a population, more significant than simply exterminating an individual cockroach.
If you're concerned about pesticides in your home because you have pets and children, you can use a simple solution of sugar and baking soda to kill them. Neither substance is harmful to humans or pets, but the solution is lethal for roaches. The sweet smell of sugar entices the roach out of hiding to eat it, as well as the baking soda. Then, when the roach drinks water, the baking soda reacts, creating gas inside of the roach which causes its stomach to burst, killing the roach. Since other roaches feed on dead roaches, they also acquire the fatal substance and subsequently die.
Counterclaim: p 5 of 6, http://lancaster.unl.edu/pest/roach/roach10eng.pdf:
Bran, baking soda, and baking powder. An old wives’ tale says that if you feed bran to insects, the bran will swell up inside the insect and it will die. There are similar claims made about baking soda and baking powder, common leavening agents used in baking. Bran, baking powder, and baking soda will not cause cockroaches to die