TOPICS
Search

Biquadratic Equation


The term "biquadratic equation" is sometimes used to as a synonym for quartic equation (Beyer 1987b, p. 34), but perhaps more commonly (e.g., Hazewinkel 1988; Gellert et al. 1989, p. 101) and more properly for a quartic equation having no odd powers, i.e.,

 z^4+a_2z^2+a_0=0.

Such equations are easy to solve, since they reduce to a quadratic equation in the variable x=z^2 and hence can be solved for x using the quadratic formula and then in terms of the original variables by taking the square roots.


See also

Quadratic Equation, Quartic Equation

Explore with Wolfram|Alpha

References

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 12, 1987a.Beyer, W. H. Handbook of Mathematical Sciences, 6th ed. Boca Raton, FL: CRC Press, 1987b.Gellert, W.; Gottwald, S.; Hellwich, M.; Kästner, H.; and Künstner, H. (Eds.). VNR Concise Encyclopedia of Mathematics, 2nd ed. New York: Van Nostrand Reinhold, 1989.Hazewinkel, M. (Managing Ed.). Encyclopaedia of Mathematics: An Updated and Annotated Translation of the Soviet "Mathematical Encyclopaedia." Dordrecht, Netherlands: Reidel, 1988.

Referenced on Wolfram|Alpha

Biquadratic Equation

Cite this as:

Weisstein, Eric W. "Biquadratic Equation." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BiquadraticEquation.html

Subject classifications