Answer: It's difficult to grow banana plants indoors; they love the heat and humidity of the tropics, which is difficult to provide in the average home during the winter months. Browning leaves usually indicate inadequate humidity or moisture. You may be able to combat that by misting the plant frequently or by setting a humidifier near the plant. It needs bright light so you may want to invest in a gro-light to supplement the winter sunshine. Some gardeners have better success in letting the plant go dormant over the winter months by setting it in a garage or basement where temperatures remain about 50F and watering sparingly rather than trying to keep it growing during the winter. In the spring they increase the water and the light and the plant breaks dormancy and begins to grow again. With your plant, I'd recommend separating the healthy new pups from the parent plant and growing those rather than trying to save the sick and stressed parent (mold is never a good sign on a plant!) Once repotted in fresh potting soil, mist the little plants once or twice a day and keep the soil moist but not soggy wet. Add some supplemental lighting, keeping it on for 14-16 hours a day. You should see some healthy growth from your plants in a few short weeks.
Best wishes with your banana plant!
Q&A Library Searching Tips