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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.
A constant coefficient, also known as constant term or simply constant, is a quantity either implicitly attached to the zeroth power of a variable or not attached to other variables in an expression; for example, the constant coefficients of the expressions above are the number 3 and the parameter c, involved in 3=c ⋅ x 0.
The highest order of derivation that appears in a (linear) differential equation is the order of the equation. The term b(x), which does not depend on the unknown function and its derivatives, is sometimes called the constant term of the equation (by analogy with algebraic equations), even when this term is a non-constant function.
The term secular function has been used for what is now called characteristic polynomial (in some literature the term secular function is still used). The term comes from the fact that the characteristic polynomial was used to calculate secular perturbations (on a time scale of a century, that is, slow compared to annual motion) of planetary ...
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).
A more explicit way to denote this function is x ↦ ax 2 + bx + c, which clarifies the function-argument status of x and the constant status of a, b and c. Since c occurs in a term that is a constant function of x, it is called the constant term. [21] Specific branches and applications of mathematics have specific naming conventions for ...
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[3] [4] The characteristic equation can only be formed when the differential or difference equation is linear and homogeneous, and has constant coefficients. [1] Such a differential equation, with y as the dependent variable , superscript ( n ) denoting n th - derivative , and a n , a n − 1 , ..., a 1 , a 0 as constants,