A triple root occurs in mathematics when a polynomial has a single root that appears three times. For example, in the polynomial equation f(x) = (x - a)³, the value x = a is a triple root. This means that the graph of the polynomial touches the x-axis at x = a but does not cross it, indicating that the root is a point of tangency. In terms of behavior, a triple root affects the shape of the graph near the root. The polynomial's derivative will also equal zero at this point, leading to a flat appearance. Understanding triple roots is essential in fields like algebra and calculus, where they help analyze polynomial functions.