Abstract

The Polynomial coefficient function Fⁿ, from Cⁿ in itself, is given by the function Fn that provides the coefficients of the polynomial (x – a1)(x – a2) ... (x – an) : Fⁿ = λa₁, a₂, ..., a_n.(b₁, b₂, ..., b_n) : π_i=1,n(x – a_i) = xⁿ + b₁x^n–1 + b₂x^n–2 + ... + b_n. A proof of the fundamental theorem of algebra is given where the surjectivity of this function is obtained from a Recurrent Coefficient Equation.

Keywords: Fundamental theorem of algebra, Recurrent equation, Polynomial coefficient function, Complex hyperspace