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In mathematics, a quartic equation is one which can be expressed as a quartic function equaling zero. The general form of a quartic equation is Graph of a polynomial function of degree 4, with its 4 roots and 3 critical points. + + + + = where a ≠ 0.
Each coordinate of the intersection points of two conic sections is a solution of a quartic equation. The same is true for the intersection of a line and a torus.It follows that quartic equations often arise in computational geometry and all related fields such as computer graphics, computer-aided design, computer-aided manufacturing and optics.
The problem may be reduced to the quartic equation x 3 (x − c) − 1 = 0, which can be solved by approximation methods, as suggested by Gardner, or the quartic may be solved in closed form by Ferrari's method. Once x is obtained, the width of the alley is readily calculated. A derivation of the quartic is given below, along with the desired ...
An algebraic solution to the problem was finally found first in 1965 by Jack M. Elkin (an actuary), by means of a quartic polynomial. [8] Other solutions were rediscovered later: in 1989, by Harald Riede; [9] in 1990 (submitted in 1988), by Miller and Vegh; [10] and in 1992, by John D. Smith [3] and also by Jörg Waldvogel. [11]
In mathematics, especially in algebraic geometry, a quartic surface is a surface defined by an equation of degree 4. More specifically there are two closely related types of quartic surface: affine and projective. An affine quartic surface is the solution set of an equation of the form (,,) =
The solution of the general quartic equation relies on the solution of its resolvent cubic. The eigenvalues of a 3×3 matrix are the roots of a cubic polynomial which is the characteristic polynomial of the matrix.
Finding the roots (zeros) of a given polynomial has been a prominent mathematical problem.. Solving linear, quadratic, cubic and quartic equations in terms of radicals and elementary arithmetic operations on the coefficients can always be done, no matter whether the roots are rational or irrational, real or complex; there are formulas that yield the required solutions.
Figure 1. Plots of quadratic function y = ax 2 + bx + c, varying each coefficient separately while the other coefficients are fixed (at values a = 1, b = 0, c = 0). A quadratic equation whose coefficients are real numbers can have either zero, one, or two distinct real-valued solutions, also called roots.
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