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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.
Therefore, the polynomial has a degree of 5, which is the highest degree of any term. To determine the degree of a polynomial that is not in standard form, such as (+) (), one can put it in standard form by expanding the products (by distributivity) and combining the like terms; for example, (+) = is of degree 1, even though each summand has ...
In arithmetic and algebra, the fifth power or sursolid [1] of a number n is the result of multiplying five instances of n together: n 5 = n × n × n × n × n. Fifth powers are also formed by multiplying a number by its fourth power, or the square of a number by its cube. The sequence of fifth powers of integers is:
Constant function: polynomial of degree zero, graph is a horizontal straight line; Linear function: First degree polynomial, graph is a straight line. Quadratic function: Second degree polynomial, graph is a parabola. Cubic function: Third degree polynomial. Quartic function: Fourth degree polynomial. Quintic function: Fifth degree polynomial.
The fact that every polynomial equation of positive degree has solutions, possibly non-real, was asserted during the 17th century, but completely proved only at the beginning of the 19th century. This is the fundamental theorem of algebra , which does not provide any tool for computing exactly the solutions, although Newton's method allows ...
Any general polynomial of degree n = + + + + (with the coefficients being real or complex numbers and a n ≠ 0) has n (not necessarily distinct) complex roots r 1, r 2, ..., r n by the fundamental theorem of algebra.
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