Preheat the oven to 350 degrees and grease 2 12-cup muffins tins pans. Set aside.
In a large bowl combing the flour, baking powder, baking soda, cinnamon and salt. Whisk to combine.
In another medium bowl combine the eggs, sugar, oil, applesauce, and bananas. Stir until well combined.
Add the egg mixture to the flour mixture and stir until just incorporated. Don't over mix at this point of the batter will get tough. Add the shredded zucchini and gently fold it into the batter. Pour the batter evenly into the prepared pans and bake for 18-24 minutes or until a toothpick inserted into the center of a muffin comes out clean.
Let the muffins cool in the pan for about 10 minutes, remove from the pan, and then let it cool some on a wire rack before serving. Store in an airtight container.