Definition

Noun: A biquadratic polynomial is a polynomial of the fourth degree. This means the highest power of the variable (usually x) in the polynomial is four (x⁴). It is also commonly called a quartic polynomial.

Usage

The term is used in algebra and mathematics to classify and describe polynomial equations. - It is typically written in the standard form: ax⁴ + bx³ + cx² + dx + e, where a, b, c, d, and e are constants, and a is not equal to zero. - The primary characteristic is its degree, which is 4.

Examples

Advanced Usage

• Biquadratic Equation: An equation set equal to zero (e.g., ) is called a biquadratic or quartic equation.
• Biquadratic Filter: In signal processing, the term "biquadratic" refers to a transfer function that is a ratio of two quadratic polynomials, not a single fourth-degree polynomial. This is a distinct, specialized usage.

Variants and Related Words

• Quartic Polynomial: A direct synonym for biquadratic polynomial.
• Biquadratic: Can function as a noun (synonymous with biquadratic polynomial) or an adjective (e.g., ).
• Polynomial: The general category.
• Quadratic Polynomial: A polynomial of the second degree ().
• Cubic Polynomial: A polynomial of the third degree ().

Synonyms

• Quartic polynomial
• Fourth-degree polynomial

Related Phrases

• To solve a biquadratic: To find the roots (solutions) of a biquadratic polynomial equation.
• Biquadratic residue: A concept in number theory related to fourth powers modulo a prime number.

Noun

1. a polynomial of the fourth degree