# Help writing algebra equations

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## Help writing algebra equations

## Equations Worksheets

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# Algebra: Writing Problems utilizing or in Algebra ( US Version ) + Resources

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# Algebraic equation

Some but non all multinomial equations with rational coefficients have a solution that is an algebraic look that can be found utilizing a finite figure of operations that involve merely those same types of coefficients ( that is, can be solved algebraically ) . This can be done for all such equations of degree one, two, three, or four ; but for degree five or more it can merely be done for some equations, non for all. A big sum of research has been devoted to calculate expeditiously accurate estimates of the existent or complex solutions of a univariate algebraic equation ( see Root-finding algorithm ) and of the common solutions of several multivariate multinomial equations ( see System of multinomial equations ) .

## History

Univariate algebraic equations over the rationals ( i.e. , with rational coefficients ) have a really long history. Ancient mathematicians wanted the solutions in the signifier of extremist looks, like x = 1 + 5 2 { \displaystyle x= { \frac { 1+ { \sqrt { 5 } } } { 2 } } } for the positive solution of x 2 − x − 1 = 0 { \displaystyle x^ { 2 } -x-1=0 } . The ancient Egyptians knew how to work out equations of degree 2 in this mode. The Indian mathematician Brahmagupta ( 597–668 AD ) explicitly described the quadratic expression in his treatise Brāhmasphuṭasiddhānta published in 628 AD, but written in words alternatively of symbols. In the ninth century Muhammad ibn Musa al-Khwarizmi and other Islamic mathematicians derived the quadratic expression, the general solution of equations of degree 2, and recognized the importance of the discriminant. During the Renaissance in 1545, Gerolamo Cardano published the solution of Scipione del Ferro and Niccolò Fontana Tartaglia to equations of degree 3 and that of Lodovico Ferrari for equations of degree 4. Finally Niels Henrik Abel proved, in 1824, that equations of degree 5 and higher do non hold general solutions utilizing groups. Galois theory, named after Évariste Galois, showed that some equations of at least degree 5 do non even have an idiosyncratic solution in groups, and gave standards for make up one's minding if an equation is in fact solvable utilizing groups.

## Areas of survey

The algebraic equations are the footing of a figure of countries of modern mathematics: Algebraic figure theory is the survey of ( univariate ) algebraic equations over the rationals ( that is, with rational coefficients ) . Galois theory has been introduced by Évariste Galois for acquiring standards make up one's minding if an algebraic equation may be solved in footings of groups. In field theory, an algebraic extension is an extension such that every component is a root of an algebraic equation over the basal field. Nonnatural figure theory is the survey of the existent Numberss which are non solutions to an algebraic equation over the rationals. A Diophantine equation is a ( normally multivariate ) multinomial equation with whole number coefficients for which one is interested in the whole number solutions. Algebraic geometry is the survey of the solutions in an algebraically closed field of multivariate multinomial equations.

## Solutions

As for any equation, the solutions of an equation are the values of the variables for which the equation is true. For univariate algebraic equations these are besides called roots, even if, decently speech production, one should state the solutions of the algebraic equation P=0 are the roots of the multinomial P. When work outing an equation, it is of import to stipulate in which set the solutions are allowed. For illustration, for an equation over the rationals one may look for solutions in which all the variables are whole numbers. In this instance the equation is a Diophantine equation. One may besides be interested merely in the existent solutions. However, for univariate algebraic equations, the figure of solutions is finite, and all solutions are contained in any algebraically closed field incorporating the coefficients—for illustration, the field of complex Numberss in the instance of equations over the rationals. It follows that without preciseness `` root '' and `` solution '' normally mean `` solution in an algebraically closed field '' .

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