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8 papers · 1 filter
On the Cubic Equation with its Siebeck--Marden--Northshield Triangle and the Quartic Equation with its Tetrahedron
Emil M. Prodanov
The real roots of the cubic and quartic polynomials are studied geometrically with the help of their respective Siebeck--Marden--Northshield equilateral triangle and regular tetrah…
On Newton's Rule of Signs
Emil M. Prodanov
Analysing the cubic sectors of a real polynomial of degree n, a modification of the Newton Rule is Signs is proposed with which stricter upper bound on the number of real roots can…
Isolation Intervals of the Real Roots of the Parametric Cubic Equation and Improved Complete Root Classification
Emil M. Prodanov
The isolation intervals of the real roots of the real symbolic monic cubic polynomial are found in terms of simple functions of the coefficients…
The Siebeck-Marden-Northshield Theorem and the Real Roots of the Symbolic Cubic Equation
Emil M. Prodanov
The isolation intervals of the real roots of the symbolic monic cubic polynomial are determined, in terms of the coefficients of the polynomial, by solving…
A Method for Locating the Real Roots of the Symbolic Quintic Equation Using Quadratic Equations
Emil M. Prodanov
A method is proposed with which the locations of the roots of the monic symbolic quintic polynomial can be determined using the ro…
New Bounds on the Real Polynomial Roots
Emil M. Prodanov
The presented analysis determines several new bounds on the roots of the equation (with ). All proposed new bounds are lower…