# Dictionary Definition

### Noun

1 an algebraic equation of the fourth degree [syn: biquadrate, quartic, fourth power]
2 an equation of the fourth degree [syn: biquadratic equation]
3 a polynomial of the fourth degree [syn: biquadratic polynomial, quartic polynomial]

# User Contributed Dictionary

## English

1. Of a polynomial expression, involving only the second and fourth powers of a variable, as x4 + 3x2 + 2. Sometimes extended to any expression involving the fourth power of variable (but no higher powers), as x4 − 4x3 + 3x2 − x + 1.

# Extensive Definition

A quartic function is a function of the form
f(x)=ax^4+bx^3+cx^2+dx+e \,
with nonzero a; or in other words, a polynomial function with a degree of four. Such a function is sometimes called a biquadratic function, but the latter term can occasionally also refer to a quadratic function of a square, having the form
ax^4+bx^2+c \,,
or a product of two quadratic factors, having the form
(ax^2+bx+c)(dy^2+ey+f) \,.
Since a quartic function is a polynomial of even degree, it has the same limit when the argument goes to positive or negative infinity. If a is positive, then the function increases to positive infinity at both sides; and thus the function has a global minimum. Likewise, if a is negative, it decreases to negative infinity and has a global maximum.
The derivative of a quartic function is a cubic function.
On finding the roots, see Quartic equation.