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Full-Text Articles in Physical Sciences and Mathematics
The Siebeck-Marden-Northshield Theorem And The Real Roots Of The Symbolic Cubic Equation, Emil Prodanov
The Siebeck-Marden-Northshield Theorem And The Real Roots Of The Symbolic Cubic Equation, Emil Prodanov
Articles
The isolation intervals of the real roots of the symbolic monic cubic polynomial x 3 ` ax2 ` 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.
A Method For Locating The Real Roots Of The Symbolic Quintic Equation Using Quadratic Equations, Emil Prodanov
A Method For Locating The Real Roots Of The Symbolic Quintic Equation Using Quadratic Equations, Emil Prodanov
Articles
A method is proposed with which the locations of the roots of the monic symbolic quintic polynomial $x^5 + a_4 x^4 + a_3 x^3 + a_2 x^2 + a_1 x + a_0$ can be determined using the roots of two {\it resolvent} quadratic polynomials: $q_1(x) = x^2 + a_4 x + a_3$ and $q_2(x) = a_2 x^2 + a_1 x + a_0$, whose coefficients are exactly those of the quintic polynomial. The different cases depend on the coefficients of $q_1(x)$ and $q_2(x)$ and on some specific relationships between them. The method is illustrated with the full analysis of one of …