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Brahmagupta gave the solution of the general linear equation in ... He went on to solve systems of ... although he explains how to find the cube and cube-root of an ...
Here the function is . In algebra, a cubic equation in one variable is an equation of the form. in which a is nonzero. The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation.
Descartes theory of geometric solution of equations uses a parabola to introduce cubic equations, in this way it is possible to set up an equation whose solution is a cube root of two. Note that the parabola itself is not constructible except by three dimensional methods.
Descartes' theorem can be expressed as a matrix equation and then generalized to other configurations of four oriented circles by changing the matrix. Let be a column vector of the four circle curvatures and let be a symmetric matrix whose coefficients represent the relative orientation between the i th and j th oriented circles at their ...
In between the rhetorical and syncopated stages of symbolic algebra, a geometric constructive algebra was developed by classical Greek and Vedic Indian mathematicians in which algebraic equations were solved through geometry. For instance, an equation of the form was solved by finding the side of a square of area.
The study of linear algebra emerged from the study of determinants, which were used to solve systems of linear equations. Calculus had two main systems of notation, each created by one of the creators: that developed by Isaac Newton and the notation developed by Gottfried Leibniz.
In mathematics, a system of linear equations (or linear system) is a collection of one or more linear equations involving the same variables. [1] For example, is a system of three equations in the three variables x, y, z. A solution to a linear system is an assignment of values to the variables such that all the equations are simultaneously ...
Descartes rule of signs and linear fractional transformations of the variable are, nowadays, the basis of the fastest algorithms for computer computation of real roots of polynomials (see real-root isolation ).