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  2. Quartic function - Wikipedia

    en.wikipedia.org/wiki/Quartic_function

    where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial. A quartic equation, or equation of the fourth degree, is an equation that equates a quartic polynomial to zero, of the form + + + + =, where a ≠ 0. [1]

  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

    The propositions for the degree of sums and products of polynomials in the above section do not apply, if any of the polynomials involved is the zero polynomial. [ 8 ] It is convenient, however, to define the degree of the zero polynomial to be negative infinity , − ∞ , {\displaystyle -\infty ,} and to introduce the arithmetic rules [ 9 ]

  5. 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 ...

  6. Quartic surface - Wikipedia

    en.wikipedia.org/wiki/Quartic_surface

    where f is a polynomial of degree 4, such as ⁠ (,,) = + + + ⁠. This is a surface in affine space A 3 . On the other hand, a projective quartic surface is a surface in projective space P 3 of the same form, but now f is a homogeneous polynomial of 4 variables of degree 4, so for example ⁠ f ( x , y , z , w ) = x 4 + y 4 + x y z w + z 2 w 2 ...

  7. Quartic plane curve - Wikipedia

    en.wikipedia.org/wiki/Quartic_plane_curve

    The cruciform curve, or cross curve is a quartic plane curve given by the equation = where a and b are two parameters determining the shape of the curve. The cruciform curve is related by a standard quadratic transformation, x ↦ 1/x, y ↦ 1/y to the ellipse a 2 x 2 + b 2 y 2 = 1, and is therefore a rational plane algebraic curve of genus zero.

  8. Curve fitting - Wikipedia

    en.wikipedia.org/wiki/Curve_fitting

    Polynomial curves fitting points generated with a sine function. The black dotted line is the "true" data, the red line is a first degree polynomial, the green line is second degree, the orange line is third degree and the blue line is fourth degree. The first degree polynomial equation = + is a line with slope a. A line will connect any two ...

  9. Vieta's formulas - Wikipedia

    en.wikipedia.org/wiki/Vieta's_formulas

    Vieta's formulas are frequently used with polynomials with coefficients in any integral domain R.Then, the quotients / belong to the field of fractions of R (and possibly are in R itself if happens to be invertible in R) and the roots are taken in an algebraically closed extension.