Bacteria that inhabit the roots of certain plants and soil play an essential role in cycling which element in an ecosystem?

The answer is nitrogen. Free-living or symbiotic bacteria known as diazotrophs 'fix' atmospheric nitrogen into nitrates and nitrites. The bacteria use an enzyme that combines gaseous nitrogen with hydrogen to produce ammonia. Ammonia is in turn converted to nitrites and nitrates through nitrification. While plants do not have access to atmospheric nitrogen, then can assimilate ammonium, nitrites and nitrates. Symbiotic bacteria can live in the root nodules of legumes and provide the host plant with ammonia in exchange for carbohydrates.