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Solving Cubic Equations Using Dynamic Geometry

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Abstract

In a right-angled triangle ABC with right angle at point B, base BC, perpendicular AB, perpendiculars BD and EF upon AC, perpendicular DE upon BC, DN upon AB, and finally perpendicular NO upon AC are drawn. When length ON is adjusted by varying angle C, so as to equate it with the constant term of the transformed cubic equation, length BD is equal to the value of one of the real roots of the equation.

Other roots can be determined from the resulting quadratic equation.

Perpendiculars BD and EF upon AC, perpendicular DE upon BC when drawn in a right-angled triangle ABC with right angle at point B, base BC, perpendicular AB, and then these perpendiculars bear a common ratio cos C given by EF/DE = DE/BD = BD/AB = cos C, where C is an angle enclosed by sides CB and CA. These ratios are exploited to solve cubic equations.

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  1. House No. 563, Sector 2, Panchkula, Haryana, 134109, India

    Narinder Kumar Wadhawan

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  1. Narinder Kumar Wadhawan
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Correspondence to Narinder Kumar Wadhawan.

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Narinder Kumar Wadhawan, although an engineering graduate, switched to civil service after a short stint with technical posts. To satisfy his passion for mathematics, he, after retirement from the Indian Administrative Service, writes research papers that have been published in reputed journals, some abstracted and indexed in WoS and Scopus.

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Wadhawan, N.K. Solving Cubic Equations Using Dynamic Geometry. Reson 29, 919–934 (2024). https://doi.org/10.1007/s12045-024-0919-2

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  • DOI: https://doi.org/10.1007/s12045-024-0919-2

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