A root of a function of one variable is the value of the argument for which the function has a zero value. The roots of some of the functions introduced in Chap. 2 play an important role in subsequent chapters and these are explored in examples and case studies. Simple examples are the polynomials in Table 2.2. The Chebyshev polynomials \(T_{n}(x)\) have roots whose locations are known, whereas the Legendre polynomials \(P_{n}(x)\) generally have roots that are not known analytically and need to be found by numerical algorithms such as those described in this chapter.