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  2. Degree of a polynomial - Wikipedia

    en.wikipedia.org/wiki/Degree_of_a_polynomial

    The degree of the exponential function, ⁡, is . The formula also gives sensible results for many combinations of such functions, e.g., the degree of + is /. Another formula to compute the degree of f from its values is

  3. Cubic equation - Wikipedia

    en.wikipedia.org/wiki/Cubic_equation

    algebraically: more precisely, they can be expressed by a cubic formula involving the four coefficients, the four basic arithmetic operations, square roots, and cube roots. (This is also true of quadratic (second-degree) and quartic (fourth-degree) equations, but not for higher-degree equations, by the Abel–Ruffini theorem.) trigonometrically

  4. Quartic function - Wikipedia

    en.wikipedia.org/wiki/Quartic_function

    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] The derivative of a quartic function is a cubic function.

  5. Quartic equation - Wikipedia

    en.wikipedia.org/wiki/Quartic_equation

    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.

  6. Quintic function - Wikipedia

    en.wikipedia.org/wiki/Quintic_function

    More generally, if an equation P(x) = 0 of prime degree p with rational coefficients is solvable in radicals, then one can define an auxiliary equation Q(y) = 0 of degree p – 1, also with rational coefficients, such that each root of P is the sum of p-th roots of the roots of Q.

  7. Septic equation - Wikipedia

    en.wikipedia.org/wiki/Septic_equation

    Septics are the lowest order equations for which it is not obvious that their solutions may be obtained by composing continuous functions of two variables. Hilbert's 13th problem was the conjecture this was not possible in the general case for seventh-degree equations. Vladimir Arnold solved this in 1957, demonstrating that this was always ...

  8. Abel–Ruffini theorem - Wikipedia

    en.wikipedia.org/wiki/Abel–Ruffini_theorem

    Polynomial equations of degree two can be solved with the quadratic formula, which has been known since antiquity. Similarly the cubic formula for degree three, and the quartic formula for degree four, were found during the 16th century. At that time a fundamental problem was whether equations of higher degree could be solved in a similar way.

  9. Sextic equation - Wikipedia

    en.wikipedia.org/wiki/Sextic_equation

    Watt's curve, which arose in the context of early work on the steam engine, is a sextic in two variables.. One method of solving the cubic equation involves transforming variables to obtain a sextic equation having terms only of degrees 6, 3, and 0, which can be solved as a quadratic equation in the cube of the variable.