quartic polynomial
Definition
Noun: A quartic polynomial is a polynomial whose highest-degree term is raised to the fourth power. It is a single-variable polynomial of degree four, meaning its general form is ( ax^4 + bx^3 + cx^2 + dx + e ), where ( a ), ( b ), ( c ), ( d ), and ( e ) are constants and ( a \neq 0 ).
Usage
The term quartic polynomial is used to classify and describe a specific type of algebraic expression based on its degree. * In algebra, solving a quartic polynomial means finding its roots (the values of x for which the polynomial equals zero). * The graph of a quartic polynomial is called a quartic curve.
Examples
Advanced Usage
- Biquadratic Polynomial: A special case of a quartic polynomial that lacks the ( x^3 ) and ( x^1 ) terms, taking the form ( ax^4 + cx^2 + e ). This type can often be solved as a quadratic in ( x^2 ).
- Quartic Equation: This refers specifically to the equation formed by setting a quartic polynomial equal to zero (e.g., ( ax^4 + bx^3 + cx^2 + dx + e = 0 )).
Variants and Related Words
- Quartic (noun/adjective): Often used interchangeably with "quartic polynomial" as a noun ("solve the quartic"), or as an adjective ("a quartic function").
- Polynomial (noun): The general category to which a quartic polynomial belongs.
- Degree (noun): The highest exponent of the variable in a polynomial. A quartic polynomial has degree four.
Synonyms
- Fourth-degree polynomial
- Polynomial of degree four
Related Terms (Not Phrasal Verbs or Idioms)
- Quadratic Polynomial: A polynomial of degree two.
- Cubic Polynomial: A polynomial of degree three.
- Quintic Polynomial: A polynomial of degree five.
- Root/Zero: A solution to the polynomial equation ( P(x) = 0 ).
Noun
-
a polynomial of the fourth degree
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