Geodesic
Intersect a quartic to extract its roots
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 16 (2017).

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In this note we present a new method for determining the roots of a quartic polynomial, wherein the curve of the given quartic polynomial is intersected by the curve of 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 
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Kulkarni, Raghavendra G. Intersect a quartic to extract its roots. Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica, no. 16 (2017). http://geodesic.mathdoc.fr/item/AUPCM_2017_16_a2/