Final answer:
Without factoring the polynomial or using numerical methods to find the roots of the given polynomial equation, we cannot determine the multiplicity of its roots.
Step-by-step explanation:
The question is asking us to find the multiplicity of the roots of the polynomial equation x³ - 9x² - 16x - 144. The multiplicity of a root refers to the number of times that root occurs as a solution to the polynomial equation. However, with the information provided and without an actual solution of the given polynomial, we can't directly determine the multiplicity of its roots.
This is typically done by factoring the polynomial or by using synthetic division to find its roots and determine their corresponding multiplicities. For the polynomial given as x³ - 9x² - 16x - 144, once we factor it (if possible) or use numerical methods to approximate its roots, we can then count the number of times each root occurs.