Free living nitrogen-fixing bacteria are found in soil and air.

Soil:
• Soil is a rich source of free living nitrogen-fixing bacteria.
• These bacteria play a crucial role in the nitrogen cycle by converting atmospheric nitrogen gas into a form that is usable by plants.
• Some common examples of free living nitrogen-fixing bacteria found in soil include Azotobacter, Clostridium, and Bacillus.

Air:
• The air also contains free living nitrogen-fixing bacteria.
• These bacteria are present in large quantities in the soil, and they are released into the air through various processes such as wind erosion and plant respiration.
• Some common examples of free living nitrogen-fixing bacteria found in the air include Azospirillum and Beijerinckia.

Root nodules:
• While some nitrogen-fixing bacteria are free-living, others form symbiotic relationships with plants, forming root nodules.
• These bacteria are called rhizobia, and they work together with the plant to fix nitrogen from the air and convert it into a usable form.
• Examples of plants that have symbiotic relationships with nitrogen-fixing bacteria include legumes such as soybeans, peas, and alfalfa.

In conclusion, free living nitrogen-fixing bacteria are found in soil and air, while some bacteria form symbiotic relationships with plants, forming root nodules.