Answer: There are several reasons it may be discoloring. It is possible it was stressed by planting into cold soil or was not sufficiently conditioned between the controlled greenhouse conditions and being planted outside, or was exposed to cold temperatures at some point. Overfertilizing can "burn" roots; over or underwatering can cause browning as well. And, wind can damage the foliage.
Bananas don't mind heat and humidity. Wind however tears the leaves and also causes water loss to speed up. It would be better to have it in a spot that is sheltered from constant winds.
Bananas have large leaves and it takes a lot of water to keep them hydrated. With a new plant, the roots may not be fully established so they may not be able to keep up with heat and wind combined. So you need to water carefully.
The soil needs to be moist, but not sopping wet or saturated. Bananas are very sensitive to poorly drained or overly wet soil. Either over or underwatering could cause it to discolor. You would need to dig into the soil with your finger and see if you need to water. Check the original potting mix and the surrouding soil as they may dry at different rates. If the soil is moist, do not water yet. When you do water, water slowly and thoroughly so it soaks down to where the deep roots are. After watering, wait a few hours and then dig down to see how far the water went; it can be surprising.
As far as which water to use, never use the softened water on plants indoors or out. The chemicals used to soften it are bad for plants.
Bananas need a rich soil, and you would use a complete,general purposed granular or slow release such as 10-10-10 or similar proportions according to the label directions. That along with a topdressing of good quality compost each spring and using an organic mulch should be sufficient. I would not recommend using a water solubler fertilizer or a high nitrogen fertilizer.
I hope this helps you trouble shoot. You might also want to consult with your retailer and/or county extension.
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