biquadratic equation

Thân thiện

A student solves a biquadratic equation on the chalkboard.

Definition

Noun: 1. A polynomial equation of the fourth degree: A biquadratic equation is an algebraic equation in which the highest power of the unknown variable is four. It is also known as a quartic equation. The general form is ( ax^4 + bx^3 + cx^2 + dx + e = 0 ), where ( a \neq 0 ).

Usage Examples

• Noun:
  • Solving a biquadratic equation can sometimes be reduced to solving two quadratic equations.
  • The mathematician presented a new method for finding the roots of a biquadratic equation.

Advanced Usage

• Biquadratic Polynomial/Function: Refers to the polynomial expression itself, ( f(x) = ax^4 + bx^3 + cx^2 + dx + e ), before it is set equal to zero to form an equation.
  • The graph of a biquadratic function may have up to three turning points.

Variants and Related Words

• Quartic Equation (n): A direct synonym for biquadratic equation.
• Biquadratic (adj): Describing something related to the fourth power.
  • The biquadratic term in the polynomial is ( 3x^4 ).
• Quadratic Equation (n): An equation of the second degree (e.g., ( ax^2 + bx + c = 0 )), which is of a lower order.

Synonyms

• Quartic Equation: The more modern and commonly used term in higher mathematics.
• Fourth-degree Equation: A descriptive synonym.

Notes on Meaning

The term "biquadratic" originates from an older naming convention where "quadratic" referred to the square (second power) of a variable. Thus, "biquadratic" literally meant "squared square" or the fourth power. While "quartic equation" is now the standard term in most mathematical contexts, "biquadratic equation" remains correct and is still used.

Học thuật

Noun

1. an equation of the fourth degree

Từ đồng nghĩa

• biquadratic