# The Fundamental Theorem of Algebra: An Elementary and Direct Proof

@article{Oliveira2011TheFT,
title={The Fundamental Theorem of Algebra: An Elementary and Direct Proof},
author={Oswaldo Rio Branco de Oliveira},
journal={The Mathematical Intelligencer},
year={2011},
volume={33},
pages={1-2}
}
• O. Oliveira
• Published 4 March 2011
• Mathematics
• The Mathematical Intelligencer
We present a simple, differentiation-free, integrationfree, trigonometryfree, direct and elementary proof of the Fundamental Theorem of Algebra. “The final publication (in The Mathematical Intelligencer, 33, No. 2 (2011), 1-2) is available at www.springerlink.com: http://www.springerlink.com/content/l1847265q2311325/”
15 Citations
The fundamental theorem of algebra: A most elementary proof
This paper shows an elementary and direct proof of the Fundamental Theorem of Algebra, via Bolzano-Weierstrass Theorem on Minima and the Binomial Formula, that avoids: any root extraction other than
The Fundamental Theorem of Algebra: From the Four Basic Operations
Abstract This paper presents an elementary and direct proof of the Fundamental Theorem of Algebra, via Weierstrass’ Theorem on Minima, that avoids the following: all root extractions, angles,
The Fundamental Theorem of Algebra: From the Four Basic Operations
An elementary and direct proof of the Fundamental Theorem of Algebra, via Weierstrass’ Theorem on Minima, that avoids the following: all root extractions, angles, non-algebraic functions, and so on.
A One-Line Proof of the Fundamental Theorem of Algebra with Newton's Method as a Consequence
A very short and simple proof of the existence of such descent direction that gives rise to Newton's method for solving a polynomial equation via modulus minimization and also makes the iterates definable at any critical point is presented.
Simple proof of existence of a complex eigenvalue of a complex square matrix …and yet another proof of the fundamental theorem of algebra with linear algebra
We give a simple proof of the existence of a complex eigenvalue of real or complex square matrices with Linear Algebra accessible to students beginning a first course on the subject, namely using j...
Some Simplifications in Basic Complex Analysis
This paper presents very simple and easy integration-free proofs in the context of Weierstrass's theory of functions, of the Maximum and Minimum Modulus Principles and Gutzmer-Parseval Inequalities
A Complex Primitive $N$th Root Of Unity: A Very Elementary Approach
This paper presents a primitive $n$th root of unity in $\mathbb C$. The approach is very elementary and avoids the following: the complex exponential function, trigonometry, and group theory. It also
The Exponential Matrix: an explicit formula by an elementary method
We show an explicit formula, with a quite easy deduction, for the exponential matrix $e^{tA}$ of a real square matrix $A$ of order $n\times n$. The elementary method developed requires neither Jordan
A formula substituting the undetermined coefficients and the annihilator methods
This article presents an easy formula for obtaining a particular solution of a linear ordinary differential equation with constant real coefficients, , where f is a function given by a linear
An Alternative Method for the Undetermined Coefficients and the Annihilator Methods
This paper exhibits a very simple formula for a particular solution of a linear ordinary differential equation with constant real coefficients, P(d/dt)x = f, f a function given by a linear