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biquadratics

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Definitions of biquadratics in various dictionaries:

noun - an algebraic equation of the fourth degree

noun - an equation of the fourth degree

noun - a polynomial of the fourth degree

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Possible Dictionary Clues
Plural form of biquadratic.

Biquadratics might refer to
In algebra, a Quartic function is a function of the form* * * * f * ( * x * ) * = * a * * x * * 4 * * * + * b * * x * * 3 * * * + * c * * x * * 2 * * * + * d * x * + * e * , * * * {\displaystyle f(x)=ax^{4}+bx^{3}+cx^{2}+dx+e,} * where a is nonzero, * which is defined by a polynomial of degree four, called a quartic polynomial. * 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 * * * * * f * ( * x * ) * = * a * * x * * 4 * * * + * c * * x * * 2 * * * + * e * . * * * {\displaystyle f(x)=ax^{4}+cx^{2}+e.} * A quartic equation, or equation of the fourth degree, is an equation that equates a quartic polynomial to zero, of the form * * * * * a * * x * * 4 * * * + * b * * x * * 3 * * * + * c * * x * * 2 * * * + * d * x * + * e * = * 0 * , * * * {\displaystyle ax^{4}+bx^{3}+cx^{2}+dx+e=0,} * where a ≠ 0. * The derivative of a quartic function is a cubic function. * 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.

Biquadratics might refer to

In algebra, a Quartic function is a function of the form*
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* {\displaystyle f(x)=ax^{4}+bx^{3}+cx^{2}+dx+e,}
* where a is nonzero,
* which is defined by a polynomial of degree four, called a quartic polynomial.
* 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
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* {\displaystyle f(x)=ax^{4}+cx^{2}+e.}
* A quartic equation, or equation of the fourth degree, is an equation that equates a quartic polynomial to zero, of the form
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* {\displaystyle ax^{4}+bx^{3}+cx^{2}+dx+e=0,}
* where a ≠ 0.
* The derivative of a quartic function is a cubic function.
* 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.

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