Authors : Sandeep Kumar

Volume/Issue : Volume 11 - 2026, Issue 8 - August

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DOI : https://doi.org/10.38124/ijisrt/26aug133

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Abstract : Vedic Mathematics offers a collection of efficient computational techniques that simplify algebraic manipulations and enhance problem-solving speed. This paper investigates the applicability of selected Vedic methods, namely Paravartya Yojayet, Lopana-Sthapanabhyam, Adyamadyena Antyamantyena, Vilokanam, and Anurupyena, for solving cubic equations. The study demonstrates that these techniques can rapidly determine roots and factorization of cubic polynomials when the equations exhibit identifiable structural characteristics such as rational roots, proportional coefficients, symmetry, or recognizable factorization patterns. Several illustrative examples are presented to compare the efficiency of Vedic approaches with conventional algebraic methods. The analysis reveals that Vedic techniques significantly reduce computational complexity and improve mathematical intuition for a broad class of structured cubic equations. However, their applicability is limited for arbitrary cubic equations lacking discernible patterns or rational roots. In such cases, classical algebraic procedures, particularly Cardano's method, remain indispensable for obtaining complete and rigorous solutions. The study concludes that Vedic methods should be viewed as complementary tools rather than universal replacements for classical cubic equation theory, combining computational elegance with analytical insight in mathematical education and research.

Keywords : Vedic Mathematics, Cubic Equations, Algebraic Factorization, Vedic Sutras, Polynomial

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