Definition

1. Adjective:

   • Relating to the fourth power: Describing a mathematical expression, equation, or function that involves a variable raised to the fourth power (x⁴).

2. Noun:

   • A polynomial of the fourth degree: An algebraic expression that is the sum of terms where the highest power of the variable is four (e.g., ax⁴ + bx³ + cx² + dx + e).
   • An equation of the fourth degree: An algebraic equation in which the highest power of the unknown variable is four (e.g., ax⁴ + bx³ + cx² + dx + e = 0).

Usage Examples

• Adjective:

  • The mathematician studied the properties of the biquadratic function.
  • This is a biquadratic expression involving the term x⁴.

• Noun:

  • Solving the biquadratic required advanced algebraic techniques.
  • The curve represented by this biquadratic is more complex than a parabola.

Advanced Usage

• "Biquadratic equation": A specific term for a polynomial equation of the fourth degree.
  • Ferrari's method is historically famous for solving the general biquadratic equation.
• "Biquadratic residue": In number theory, an integer is a biquadratic residue modulo a prime if there exists an integer whose fourth power is congruent to it modulo that prime.
  • The concept of a biquadratic residue extends the idea of quadratic residues.

Variants and Related Words

• Biquadrate (n): A less common synonym for the fourth power of a number (e.g., The biquadrate of 2 is 16).
• Quartic (adj/n): A more common synonym in modern mathematics for both the adjective ("quartic function") and the noun ("a quartic").

Synonyms

• Quartic: (Adjective/Noun) Pertaining to the fourth degree or power. This is the most direct and frequently used synonym.
• Fourth-degree: (Adjective) Describing a polynomial or equation.

Related Phrases

• Biquadratic polynomial: Equivalent to "quartic polynomial."
• Biquadratic curve: A curve defined by a quartic equation.

Adjective

1. of or relating to the fourth power

Noun

1. a polynomial of the fourth degree
2. an equation of the fourth degree
3. an algebraic equation of the fourth degree