Algebra/Chapter 10/Symmetric Polynomials/Elementary Symmetric Polynomials

Let there be a polynomial of degree By the Fundamental Theorem of Algebra, it has complex roots (with multiplicity). Then we can write: As we know, Vieta's formulae link between the coefficients and roots of a polynomial: As we can see, these sums are symmetric polynomial, and are called elementary symmetric polynomials. Definition The elementary symmetric polynomials in variables , are defined as such: Elementary Symmetric Polynomials Permutations and Symmetry Fundamental Theorem of Symmetric Polynomials