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In mathematics, a quadratic equation is a polynomial equation of the second degree.The general form is + + =, where a ≠ 0.. The quadratic equation on a number can be solved using the well-known quadratic formula, which can be derived by completing the square.
When there is only one variable, polynomial equations have the form P(x) = 0, where P is a polynomial, and linear equations have the form ax + b = 0, where a and b are parameters. To solve equations from either family, one uses algorithmic or geometric techniques that originate from linear algebra or mathematical analysis.
In mathematics, to solve an equation is to find its solutions, which are the values (numbers, functions, sets, etc.) that fulfill the condition stated by the equation, consisting generally of two expressions related by an equals sign. When seeking a solution, one or more variables are designated as unknowns. A solution is an assignment of ...
In mathematics, an algebraic expression is an expression built up from constants (usually, algebraic numbers) variables, and the basic algebraic operations: addition (+), subtraction (-), multiplication (×), division (÷), whole number powers, and roots (fractional powers).
Multiplication symbols are usually omitted, and implied, when there is no operator between two variables or terms, or when a coefficient is used. For example, 3 × x 2 is written as 3x 2, and 2 × x × y is written as 2xy. [5] Sometimes, multiplication symbols are replaced with either a dot or center-dot, so that x × y is written as either x.
An expression is often used to define a function, by taking the variables to be arguments, or inputs, of the function, and assigning the output to be the evaluation of the resulting expression. [5] For example, x ↦ x 2 + 1 {\displaystyle x\mapsto x^{2}+1} and f ( x ) = x 2 + 1 {\displaystyle f(x)=x^{2}+1} define the function that associates ...