CHAPTER TEN - ROOTS OF POLYNOMIALS

Abstract

The polynomial function f(x) = ax+b is called a linear function, and the polynomial function g(x) = ax2 + bx + c, a ≠ 0 is called a quadratic function. To facilitate the study of polynomial functions in general, this chapter presents the notation P(x) = anxn·+ an–1xn–1 + … + a1x + a0, an ≠ 0 as a representation of a polynomial function of degree n. The coefficient ak may be real or complex numbers and that the subscript k of the coefficient ak is the same as the exponent of x in xk. This chapter discusses the method to find the roots or solutions of the polynomial equation of degree an xn + an–1xn–1 + … + a1x +a0 = 0. These solutions are also known as the roots or zeros of the polynomial. The chapter discusses the number of roots of a polynomial in the field of complex numbers and in the field of real numbers, the number of roots in the field of rational numbers if the coefficients of a polynomial are integers, and whether there is a relationship between the roots and factors of a polynomial.