Intersect a quartic to extract its roots
Abstract
In this note we present a new method for determining the roots of a quartic polynomial, wherein the given quartic polynomial is intersected by a quadratic polynomial (which has two unknown coefficients) at its root point; so the root satisfies both the quartic and the quadratic equations. Elimination of the root term from the two equations leads to an expression in the two unknowns of quadratic polynomial. In addition, we introduce another expression in one unknown, which leads to determination of the two unknowns and subsequently the roots of quartic polynomial.
Keywords
Intersection of curves; quartic polynomial; quadratic polynomial; roots; resolvent cubic equation
Mathematics Subject Classification (2010)
12E05, 12E12
References
Dickson, Leonard E. First course in the theory of equations. New York: J. Wiley & sons, inc., 1922.
Kulkarni, Raghavendra G. "Shifting the origin to solve quartic equations." The Mathematical Gazette 97, no. 539 (2013): 268-270.
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This article by Raghavendra G. Kulkarni is governed by the Creative Commons Attribution-ShareAlike 4.0 International(CC BY-SA 4.0) licence.