biquadratic

/,baikwɔ'drætik/
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Thân thiện
biquadratic

A student graphs a biquadratic equation on the coordinate plane.

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.
biquadratic

A student graphs a biquadratic equation on the coordinate plane.

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

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