Bibliography for Roots of Quartic Equations

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  1. Reciprocal solution of a quartic equation.
    Mochimaru, Yoshihiro
    Int. J. Pure Appl. Math. 14 (2004), no. 2, 209--212, MathSciNet.  
  2. On the general solution of a quartic functional equation.
    Chung, Jukang K.; Sahoo, Prasanna K.
    Bull. Korean Math. Soc. 40 (2003), no. 4, 565--576, MathSciNet.  
  3. Method for finding roots of quartic equation with application to RS codes
    Yan, F.Y.; Ko, C.C.
    Electronics Letters, v 34, n 25, Dec 10, 1998, p 2399-2400, Compendex.
  4. Beyond the quartic equation.
    King, R. Bruce
    Birkhäuser Boston, Inc., Boston, MA, 1996. viii+149 pp., MathSciNet.  
  5. Identities for the solution of cubic and quartic equations. (Spanish)
    Sáenz Cetina, José Leonardo
    Miscelánea Mat. No. 24 (1996), 39--43, MathSciNet.  
  6. 48 More Solutions of Martin Davis's Quaternary Quartic Equation  
    Daniel Shanks; Samuel S. Wagstaff, Jr.
    Mathematics of Computation, Vol. 64, No. 212 (Oct., 1995), pp. 1717-1731, Jstor.   
  7. Khayyam, al-Biruni, Gauss, Archimedes, and quartic equations  
    Amir-Moéz, Ali R.
    Texas J. Sci. 46 (1994), no. 3, 241--257, MathSciNet.  
  8. An extension of Omar Khayyam's graphical solution of the cubic equation to the solution of the quartic
    Yardley, Peter D.
    Bull. Inst. Math. Appl. 27 (1991), no. 8-9, 173--174, MathSciNet.  
  9. A unified approach for solving quadratic, cubic and quartic equations by radicals  
    Ungar, A. A.
    International Journal of Computer Mathematics Appl. 19 (1990), no. 12, 33--39, Compendex.
  10. Some quartic equations with only trivial solutions.
    Sinha, T. N.; Singh, M. M.
    Math. Student 53 (1985), no. 1-4, 239--242 (1987), MathSciNet.  
  11. Necessary and sufficient conditions for the existence of real roots of a quartic equation.
    Zeheb, E.
    Internat. J. Circuit Theory Appl. 10 (1982), no. 3, 289--291, MathSciNet.  
  12. Root Location Criteria For Quartic Equations
    Fuller, A. T.
    IEEE Transactions on Automatic Control, v AC-26, no. 3, (June 1981), p 777-782, Compendex.  
  13. Some quartic equations with only trivial integer solutions.
    Sinha, T. N.
    Math. Student 43 (1975), 61--64 (1976), MathSciNet.  
  14. The Solution of a Certain Quartic Equation  
    B. Fisher
    Mathematics Magazine, Vol. 45, No. 2 (Mar., 1972), pp. 97-98, Jstor.   
  15. A note on the solution of quartic equations.
    Salzer, Herbert E.
    Math. Comput. 14 1960 279--281, MathSciNet.  
  16. Solvability of quartics by means of square roots.
    Borofsky, Samuel
    Amer. Math. Monthly 57, (1950). 248--250, MathSciNet.  
  17. Numerical solution of complex roots of quartic equations.
    Lin, Shih-Nge
    J. Math. Physics 26, (1948). 279--283, MathSciNet.  
  18. A comparison of methods for evaluating the complex roots of quartic equations.
    Sharp, Henry S.
    J. Math. Phys. Mass. Inst. Tech. 20, (1941). 243--258., MathSciNet.  
  19. On the Nature of the Roots of a Quartic Equation  
    Raymond Garver
    Mathematics News Letter, Vol. 7, No. 4 (Jan., 1933), pp. 6-8, Jstor.   
  20. Enrique Cruchaga's Solution of the Quartic Equation  
    Raymond Garver
    The American Mathematical Monthly, Vol. 37, No. 6 (Jun., 1930), pp. 303-304, Jstor.   
  21. Discussions: A Solution of the Quartic Equation  
    Raymond Garver
    The American Mathematical Monthly, Vol. 35, No. 10 (Dec., 1928), pp. 558-560, Jstor.   
  22. Graphical Discussion of the Roots of a Quartic Equation  
    E. L. Rees
    The American Mathematical Monthly, Vol. 29, No. 2 (Feb., 1922), pp. 51-55, Jstor.   
  23. The Asymptotic Equation and Satellite Conic of the Plane Quartic  
    Teresa Cohen
    American Journal of Mathematics, Vol. 38, No. 3 (Jul., 1916), pp. 325-336, Jstor.   
  24. On the Reciprocal Quartic Equation  
    R. L. Berger
    The American Mathematical Monthly, Vol. 15, No. 4 (Apr., 1908), pp. 85-87, Jstor.   
  25. The Galois Group of a Reciprocal Quartic Equation  
    L. E. Dickson
    The American Mathematical Monthly, Vol. 15, No. 4 (Apr., 1908), pp. 71-78, Jstor.   
  26. Condition in Terms of the Invariants of the Quartic that its Four Distinct Root-Points be Concyclic  
    T. E. McKinney
    The American Mathematical Monthly, Vol. 14, No. 2 (Feb., 1907), p. 23, Jstor.   
  27. A Graphical Method of Deducing the Criteria for the Nature of the Roots of Cubic and Quartic Equations  
    R. E. Gaines
    The Annals of Mathematics, 2nd Ser., Vol. 1, No. 1/4 (1899), pp. 111-112, Jstor.   
  28. The Deduction of Final Formulas for the Algebraic Solution of the Quartic Equation   
    Mansfield Merriman
    American Journal of Mathematics, Vol. 14, No. 3 (Jul., 1892), pp. 237-245, Jstor.   
  29. On the Bicircular Quartic. Addition to Professor Casey's Memoir "On a New Form of Tangential Equation"  
    Professor Casey's; A. Cayley
    Philosophical Transactions of the Royal Society of London, Vol. 167 (1877), pp. 441-460, Jstor.   
  30. Solution of the Quartic Equation, x^4 + Ax + B = 0  
    A. M. Sawin
    The Annals of Mathematics, Vol. 1, No. 1 (Mar., 1884), pp. 14-15, Jstor.   
  31. On the Conditions for the Existence of Three Equal Roots, or of Two Pairs of Equal Roots, of a Binary Quartic or Quintic  
    A. Cayley
    Philosophical Transactions of the Royal Society of London, Vol. 158 (1868), pp. 577-588, Jstor.   
  32. Note by Professor Cayley on His Memoir on the Conditions for the Existence of Three Equal Roots, or of Two Pairs of Equal Roots, of a Binary Quartic or Quintic  
    Professor Cayley
    Proceedings of the Royal Society of London, Vol. 17 (1868), p. 314, Jstor.   
  33. On the Conditions for the Existence of Three Equal Roots, or of Two Pairs of Equal Roots of a Binary Quartic or Quintic. [Abstract]  
    A. Cayley
    Proceedings of the Royal Society of London, Vol. 16 (1867), p. 229, Jstor.   

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2006