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If the constant term is 0, then it will conventionally be omitted when the quadratic is written out. Any polynomial written in standard form has a unique constant term, which can be considered a coefficient of . In particular, the constant term will always be the lowest degree term of the polynomial. This also applies to multivariate polynomials.
In this example a, b and c are coefficients of the polynomial. Since c occurs in a term that does not involve x, it is called the constant term of the polynomial and can be thought of as the coefficient of x 0. More generally, any polynomial term or expression of degree zero (no variable) is a constant. [5]: 18
A term with no indeterminates and a polynomial with no indeterminates are called, respectively, a constant term and a constant polynomial. [b] The degree of a constant term and of a nonzero constant polynomial is 0. The degree of the zero polynomial 0 (which has no terms at all) is generally treated as not defined (but see below).
The graph of the constant function y = c is a horizontal line in the plane that passes through the point (0, c). [2] In the context of a polynomial in one variable x, the constant function is called non-zero constant function because it is a polynomial of degree 0, and its general form is f(x) = c, where c is nonzero.
In mathematics (including combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients [1]: ch. 17 [2]: ch. 10 (also known as a linear recurrence relation or linear difference equation) sets equal to 0 a polynomial that is linear in the various iterates of a variable—that is, in the values of the elements of a sequence.
takes a negative value for some positive real value of x. In the remaining of the section, suppose that a 0 ≠ 0. If it is not the case, zero is a root, and the localization of the other roots may be studied by dividing the polynomial by a power of the indeterminate, getting a polynomial with a nonzero constant term.
If the coefficient of the variable is not zero (a ≠ 0), then a linear function is represented by a degree 1 polynomial (also called a linear polynomial), otherwise it is a constant function – also a polynomial function, but of zero degree. A straight line, when drawn in a different kind of coordinate system may represent other functions.
For example, the constant π may be defined as the ratio of the length of a circle's circumference to its diameter. The following list includes a decimal expansion and set containing each number, ordered by year of discovery. The column headings may be clicked to sort the table alphabetically, by decimal value, or by set.