Grease 2 8x4 inch loaf pans and preheat the oven to 350 degrees.
In a small bowl, stir together the flour, baking soda, cinnamon, and salt. Set aside.
In a large bowl, combine the eggs, syrup, banana, melted butter or oil, water, and vanilla extract. Add the dry ingredients and stir to combine evenly.
Stir in the grated zucchini and carrots.
Divide the batter evenly between the 2 loaf pans.
Bake for 45 to 50 minutes, or until a toothpick inserted in the center of the loaves comes out clean.
Cool on a wire rack. Store in an airtight container at room temperature for up to 3 days, or store in the freezer for up to 6 months.