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; "Ferrari-Cardano derivation of the quartic formula" is owned by djao. ... Cross-references: quadratic equation, square root, cubic formula, roots, discriminant, polynomial, perfect square, right hand side, addition, clear, square, complete, side, equation, solution, transformation, quartic equation;
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planetmath.org/encyclopedia/FerrariCardanoDerivationOfT...
planetmath.org/encyclopedia/FerrariCardanoDerivationOfTheQuarticFormula.html
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Quartic function - Wikipedia, the free encyclopedia
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In mathematics, a quartic function is a function of the form where a is nonzero; or in other words, a polynomial of degree of four. Such a function is sometimes called a biquadratic function , b...
en.wikipedia.org/wiki/Quartic_function
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The other two roots (real or complex) can then be found by polynomial division and the quadratic formula. The solution proceeds in two steps. First, the quartic equation is "depressed"; then one reduces the problem to solving a related cubic equation.
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www.sosmath.com/algebra/factor/fac12/fac12.html
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Exercise 1. Find the resolvent cubic polynomial for the depressed quartic equation ... Check that z=3 is a root of the resolvent cubic for the equation, then find all roots of the quartic equation.
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www.sosmath.com/algebra/factor/fac12a1/fac12a1.html
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Article on Quartic Formula ... The formulas for the roots are much too unwieldy to be used for solving quartic equations by radicals, even with the help of a computer. A practical algorithm for solving quartic equations by radicals is given in the concluding paragraph of the Galois-theoretic derivation of the quartic formula.
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myyn.org/m/article/quartic-formula/
myyn.org/m/article/quartic-formula/
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The Quartic Formula (10 Feb 2005 at 17:55) ... Man, did you ever want to solve an equation of the form x4 + ax3 + bx2 + cx + d = 0? Yeah? Well, no problem---just use this handy formula! (Don't forget to scroll right...)
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radar.spacebar.org/f/a/weblog/comment/1/711
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A very nice demonstration of said quartic formula, but it involves symmetric polynomials and a little bit of Galois theory, so perhaps might be somewhat abstract. This setup is so much nicer than looking at the general solution (ugh) but really amounts to the same thing.
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www.stumbleupon.com/url/planetmath.org/encyclopedia/Gal...
www.stumbleupon.com/url/planetmath.org/encyclopedia/GaloisTheoreticDerivationOfTheQuarticFormula.html
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The cubic and quartic formulas were discovered in the middle ages. ... Next: Higher degree case Up: Explicit formulas for the Previous: Cubic formula Contents Index...
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www.usna.edu/Users/math/wdj/book/node95.html
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The method for for finding the zeros of a quartic (4th degree) polynomial is given here. ... Only once in my life have I actually found use of the quartic formula. But seeing how to develop a solution to the general quartic is much more interesting than the formula itself, which is what I will do here.
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www.karlscalculus.org/quartic.html
www.karlscalculus.org/quartic.html
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