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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 other words, a quintic function is defined by a polynomial of degree five. Because they have an odd degree, normal quintic functions appear similar to normal cubic functions when graphed, except they may possess one additional local maximum and one additional local minimum. The derivative of a quintic function is a quartic function.
The values of trigonometric functions of angles related to / satisfy cubic equations. Given the cosine (or other trigonometric function) of an arbitrary angle, the cosine of one-third of that angle is one of the roots of a cubic. The solution of the general quartic equation relies on the solution of its resolvent cubic.
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Thus root-finding algorithms can be used to solve any equation of continuous functions. However, most root-finding algorithms do not guarantee that they will find all roots of a function, and if such an algorithm does not find any root, that does not necessarily mean that no root exists.
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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