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quartic equation - перевод на арабский
![minima]] were above the ''x'' axis, or if the local [[maximum]] were below it, or if there were no local maximum and one minimum below the ''x'' axis, there would only be two real roots (and two complex roots). If all three local extrema were above the ''x'' axis, or if there were no local maximum and one minimum above the ''x'' axis, there would be no real root (and four complex roots). The same reasoning applies in reverse to polynomial with a negative quartic coefficient.](https://commons.wikimedia.org/wiki/Special:FilePath/Polynomialdeg4.svg?width=200 "minima]] were above the ''x'' axis, or if the local [[maximum]] were below it, or if there were no local maximum and one minimum below the ''x'' axis, there would only be two real roots (and two complex roots). If all three local extrema were above the ''x'' axis, or if there were no local maximum and one minimum above the ''x'' axis, there would be no real root (and four complex roots). The same reasoning applies in reverse to polynomial with a negative quartic coefficient.")
![This illustration of a mechanism for acid-catalyzed [[hydrolysis]] of an [[amide]] puts some reactants and products above the arrows and to their branches to allow chaining of the chemical "equations".](https://commons.wikimedia.org/wiki/Special:FilePath/Acid-CatAmideHydrolMarch.png?width=200 "This illustration of a mechanism for acid-catalyzed [[hydrolysis]] of an [[amide]] puts some reactants and products above the arrows and to their branches to allow chaining of the chemical \"equations\".")
![base]] as a [[catalyst]].](https://commons.wikimedia.org/wiki/Special:FilePath/Baker-Venkataraman-Rearrangement V.1.svg?width=200 "base]] as a [[catalyst]].")
![water]] on the products side in order for, as per the law of conservation of mass, the quantity of each element does not change during the reaction](https://commons.wikimedia.org/wiki/Special:FilePath/Combustion reaction of methane.jpg?width=200 "water]] on the products side in order for, as per the law of conservation of mass, the quantity of each element does not change during the reaction")
![H<sub>3</sub>PO<sub>4</sub>]]<br>This chemical equation is being balanced by first multiplying H<sub>3</sub>PO<sub>4</sub> by four to match the number of P atoms, and then multiplying H<sub>2</sub>O by six to match the numbers of H and O atoms.](https://commons.wikimedia.org/wiki/Special:FilePath/H3PO4 balancing chemical equation phosphorus pentoxide and water becomes phosphoric acid.gif?width=200 "H<sub>3</sub>PO<sub>4</sub>]]<br>This chemical equation is being balanced by first multiplying H<sub>3</sub>PO<sub>4</sub> by four to match the number of P atoms, and then multiplying H<sub>2</sub>O by six to match the numbers of H and O atoms.")
Определение
Википедия
In algebra, a quartic function is a function of the form
where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial.
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. 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
Since a quartic function is defined by a polynomial of even degree, it has the same infinite limit when the argument goes to positive or negative infinity. If a is positive, then the function increases to positive infinity at both ends; and thus the function has a global minimum. Likewise, if a is negative, it decreases to negative infinity and has a global maximum. In both cases it may or may not have another local maximum and another local minimum.
The degree four (quartic case) is the highest degree such that every polynomial equation can be solved by radicals, according to the Abel–Ruffini theorem.
