Maybe this belongs in the container garden section, if so, I apologize.

I am curious if there is a problem with putting a Red Alpine Strawberry (Fragaria vesca 'Rugen') and Chives (Allium schoenoprasum and tuberosum) with a 4ft Japanese Banana plant (Musa basjoo) in a 4 sq.ft. container together. I am primarily concerned with invasive roots from the strawberry being detrimental to the banana.

Thanks in advance!