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  2. Quartic function - Wikipedia

    en.wikipedia.org/wiki/Quartic_function

    Graph of a polynomial of degree 4, with 3 critical points and four real roots (crossings of the x axis) (and thus no complex roots). If one or the other of the local minima were above the x axis, or if the local maximum were below it, or if there were no local maximum and one minimum below the x axis, there would only be two real roots (and two complex roots).

  3. Quartic equation - Wikipedia

    en.wikipedia.org/wiki/Quartic_equation

    Graph of a polynomial function of degree 4, with its 4 roots and 3 critical points. + + + + = where a ≠ 0. The quartic is the highest order polynomial equation that can be solved by radicals in the general case (i.e., one in which the coefficients can take any value).

  4. Degree of a polynomial - Wikipedia

    en.wikipedia.org/wiki/Degree_of_a_polynomial

    For polynomials in two or more variables, the degree of a term is the sum of the exponents of the variables in the term; the degree (sometimes called the total degree) of the polynomial is again the maximum of the degrees of all terms in the polynomial. For example, the polynomial x 2 y 2 + 3x 3 + 4y has degree 4, the same degree as the term x ...

  5. Quadratic formula - Wikipedia

    en.wikipedia.org/wiki/Quadratic_formula

    A similar but more complicated method works for cubic equations, which have three resolvents and a quadratic equation (the "resolving polynomial") relating ⁠ ⁠ and ⁠ ⁠, which one can solve by the quadratic equation, and similarly for a quartic equation (degree 4), whose resolving polynomial is a cubic, which can in turn be solved. [14]

  6. Quartic surface - Wikipedia

    en.wikipedia.org/wiki/Quartic_surface

    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 (,,) =

  7. Polynomial - Wikipedia

    en.wikipedia.org/wiki/Polynomial

    Polynomials of degree one, two or three are respectively linear polynomials, quadratic polynomials and cubic polynomials. [8] For higher degrees, the specific names are not commonly used, although quartic polynomial (for degree four) and quintic polynomial (for degree five) are sometimes used. The names for the degrees may be applied to the ...

  8. Quintic function - Wikipedia

    en.wikipedia.org/wiki/Quintic_function

    Chapter 8 (The solution of equations of the fifth degree at the Wayback Machine (archived 31 March 2010)) gives a description of the solution of solvable quintics x 5 + cx + d. Victor S. Adamchik and David J. Jeffrey, "Polynomial transformations of Tschirnhaus, Bring and Jerrard," ACM SIGSAM Bulletin, Vol. 37, No. 3, September 2003, pp. 90–94.

  9. System of polynomial equations - Wikipedia

    en.wikipedia.org/wiki/System_of_polynomial_equations

    The Barth surface, shown in the figure is the geometric representation of the solutions of a polynomial system reduced to a single equation of degree 6 in 3 variables. Some of its numerous singular points are visible on the image. They are the solutions of a system of 4 equations of degree 5 in 3 variables.