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The Heaviside step function is an often-used step function. A constant function is a trivial example of a step function. Then there is only one interval, =. The sign function sgn(x), which is −1 for negative numbers and +1 for positive numbers, and is the simplest non-constant step function.
It is an example of the general class of step functions, all of which can be represented as linear combinations of translations of this one. The function was originally developed in operational calculus for the solution of differential equations , where it represents a signal that switches on at a specified time and stays switched on indefinitely.
An algebraic equation or polynomial equation is an equation in which both sides are polynomials (see also system of polynomial equations). These are further classified by degree: linear equation for degree one; quadratic equation for degree two; cubic equation for degree three; quartic equation for degree four; quintic equation for degree five
Animation depicting the process of completing the square. (Details, animated GIF version)In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form + + to the form + for some values of and . [1]
In mathematics, an algebraic equation or polynomial equation is an equation of the form =, where P is a polynomial with coefficients in some field, often the field of the rational numbers. For example, x 5 − 3 x + 1 = 0 {\displaystyle x^{5}-3x+1=0} is an algebraic equation with integer coefficients and
For example, the equation = describes a line in two-dimensional space while the equation + + = corresponds to a sphere in three-dimensional space. Of special interest to algebraic geometry are algebraic varieties , [ t ] which are solutions to systems of polynomial equations that can be used to describe more complex geometric figures. [ 124 ]