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The degree of the zero polynomial 0 (which has no terms at all) is generally treated as not defined (but see below). [9] For example: is a term. The coefficient is −5, the indeterminates are x and y, the degree of x is two, while the degree of y is one.
Coefficient: An expression multiplying one of the monomials of the polynomial. Root (or zero) of a polynomial: Given a polynomial p(x), the x values that satisfy p(x) = 0 are called roots (or zeroes) of the polynomial p. Graphing. End behaviour – Concavity – Orientation – Tangency point – Inflection point – Point where concavity changes.
Kirchhoff's diffraction formula; Klein–Gordon equation; Korteweg–de Vries equation; Landau–Lifshitz–Gilbert equation; Lane–Emden equation; Langevin equation; Levy–Mises equations; Lindblad equation; Lorentz equation; Maxwell's equations; Maxwell's relations; Newton's laws of motion; Navier–Stokes equations; Reynolds-averaged ...
Polynomials: Can be generated solely by addition, multiplication, and raising to the power of a positive integer. Constant function: polynomial of degree zero, graph is a horizontal straight line; Linear function: First degree polynomial, graph is a straight line. Quadratic function: Second degree polynomial, graph is a parabola.
For a long time, the main problem was to find the solutions of a single non-linear polynomial equation in a single unknown. The fact that a complex solution always exists is the fundamental theorem of algebra , which was proved only at the beginning of the 19th century and does not have a purely algebraic proof.
Mahler polynomial; Maitland function; Émile Léonard Mathieu: Mathieu function; F. G. Mehler, student of Dirichlet (Ferdinand): Mehler's formula, Mehler–Fock formula, Mehler–Heine formula, Mehler functions. Meijer G-function; Josef Meixner: Meixner polynomial, Meixner-Pollaczek polynomial; Mittag-Leffler: Mittag-Leffler polynomials. Mott ...
The roots of a polynomial expression of degree n, or equivalently the solutions of a polynomial equation, can always be written as algebraic expressions if n < 5 (see quadratic formula, cubic function, and quartic equation). Such a solution of an equation is called an algebraic solution.
This is a list of notable theorems. Lists of theorems and similar statements include: List of algebras; List of algorithms; List of axioms; List of conjectures; List of data structures; List of derivatives and integrals in alternative calculi; List of equations; List of fundamental theorems; List of hypotheses; List of inequalities; Lists of ...