A quintic function is a polynomial function of degree five, written in the general form ax^5 + bx^4 + cx^3 + dx^2 + ex + f with a nonzero. Its graph resembles a cubic function's but can show one extra local maximum and minimum, and its derivative is a quartic polynomial. The central mathematical fact about quintics is the Abel-Ruffini theorem, first asserted in 1799 and fully proved by 1824, which shows that no general quintic equation can be solved by a formula using only radicals, unlike linear, quadratic, cubic and quartic equations. Some special quintics remain solvable by radicals, and the general quintic can still be solved using more advanced tools such as elliptic functions or the Bring radical. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
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In mathematics, a quintic function is a function of the form g ( x ) = a x 5 + b x 4 + c x 3 + d x 2 + e x + f , {\displaystyle g(x)=ax^{5}+bx^{4}+cx^{3}+dx^{2}+ex+f,\,} where a, b, c, d, e and f are members of a field, typically the rational numbers, the real numbers or the complex numbers, and a is nonzero.
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