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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 The general form of a quartic equation is Graph of a polynomial function of degree 4, with its 4 roots and 3 critical points .
The derivative of a quartic function is a cubic function. Sometimes the term biquadratic is used instead of quartic, but, usually, biquadratic function refers to a quadratic function of a square (or, equivalently, to the function defined by a quartic polynomial without terms of odd degree), having the form
In some cases, the concept of resolvent cubic is defined only when P(x) is a quartic in depressed form—that is, when a 3 = 0. Note that the fourth and fifth definitions below also make sense and that the relationship between these resolvent cubics and P ( x ) are still valid if the characteristic of k is equal to 2 .
Critical points of a quartic function are found by solving a cubic equation (the derivative set equal to zero). Inflection points of a quintic function are the solution of a cubic equation (the second derivative set equal to zero).
Solving quintic equations in terms of radicals (nth roots) was a major problem in algebra from the 16th century, when cubic and quartic equations were solved, until the first half of the 19th century, when the impossibility of such a general solution was proved with the Abel–Ruffini theorem.
There exist algebraic solutions for cubic equations [1] and quartic equations, [2] which are more complicated than the quadratic formula. The Abel–Ruffini theorem, [3]: 211 and, more generally Galois theory, state that some quintic equations, such as + =, do not have any algebraic solution.
Taiwan's digital ministry said on Friday that government departments should not use Chinese startup DeepSeek's artificial intelligence (AI) service, saying that as the product is from China it ...
In mathematics, the term quartic describes something that pertains to the "fourth order", such as the function . It may refer to one of the following: Quartic function, a polynomial function of degree 4; Quartic equation, a polynomial equation of degree 4; Quartic curve, an algebraic curve of degree 4