The Siebeck-Marden-Northshield Theorem and the Real Roots of the Symbolic Cubic Equation

Abstract

The isolation intervals of the real roots of the symbolic monic cubic polynomial $x^3+a{x}^2+bx+c$ are determined, in terms of the coefficients of the polynomial, by solving the Siebeck-Marden-Northshield triangle - the equilateral triangle that projects onto the three real roots of the cubic polynomial and whose inscribed circle projects onto an interval with endpoints equal to stationary points of the polynomial

11 pages, 8 figures

References in corpus (2)

• A Method for Locating the Real Roots of the Symbolic Quintic Equation Using Quadratic Equations
• New Bounds on the Real Polynomial Roots

Cited by in corpus (5)

• Mathematical Analysis of the van der Waals Equation
• Isolation Intervals of the Real Roots of the Parametric Cubic Equation and Improved Complete Root Classification
• On the Cubic Equation with its Siebeck--Marden--Northshield Triangle and the Quartic Equation with its Tetrahedron
• On Newton's Rule of Signs
• Three-layer water flows: Dirichlet-Neumann operators and approximations