quartic

Thân thiện

A mathematician writes a quartic equation on the chalkboard.

Definition

1. Noun:
   • An algebraic equation of the fourth degree: A "quartic" is a polynomial equation where the highest power of the variable (usually x) is four. Its general form is ax⁴ + bx³ + cx² + dx + e = 0, where a, b, c, d, and e are constants and a is not zero.

Usage Examples

• Noun:
  • Solving a quartic can be more complex than solving a quadratic equation.
  • The mathematician derived the formula for the roots of the general quartic.

Advanced Usage

• Quartic function: Refers to a polynomial function of degree four, .
  • The graph of a quartic function can have up to three turning points.
• Quartic curve/surface: In geometry, a curve or surface defined by a quartic equation.
  • The study of quartic curves is a topic in algebraic geometry.

Variants and Related Words

• Biquadratic (adj/noun): Another term for "quartic," especially an equation of the form .
  • The biquadratic equation is a special case of the quartic.
• Quartic (adjective): Describing something related to the fourth degree or fourth power.
  • The term 'quartic' comes from the Latin root for 'four'.

Synonyms

• Fourth-degree equation: A direct descriptive synonym.
• Biquadratic equation: A synonym, particularly for simpler forms.

Related Phrases

• Quartic polynomial: The polynomial expression itself, before being set equal to zero.
  • Factoring the quartic polynomial was the first step.
• Quartic formula: The formula providing the roots for a general quartic equation.
  • The quartic formula is much more elaborate than the quadratic formula.

Học thuật

Noun

1. an algebraic equation of the fourth degree

Từ đồng nghĩa

• biquadrate
• biquadratic
• fourth power