A new Proof of the Fundamental Theorem of Algebra

Jyothiniranjan Pillay

Firstly, we introduce a method, which we use to analyse the factors of polynomial functions P(x). We then establish criteria for when the zeros of P(x) with real coefficients are Real. Then finally we go on to analyse P(x) with complex coefficients by using the same method introduced. Upon completion of our analysis we would have established that P(x) with real or complex coefficients, or a mixture of both, has at least one zero i.e at least one factor.

Mots clés: Polynomial Roots of

Domaines: Mathématiques générales [math.GM]

Jyothiniranjan Pillay. A new Proof of the Fundamental Theorem of Algebra. UP Technical Reference, 2000, pp.42. ⟨hal-00655631v3⟩