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In elementary algebra, the quadratic formula is a formula that provides the solution(s) to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring (direct factoring, grouping, AC method), completing the square, graphing and others. Given a general quadratic equation of the form ax²+bx+c=0 with x representing an unknown, a, b and c representing constants with a ≠ 0, the quadratic formula is: x=(-b±√(b²-4ac))/2a where the plus–minus symbol "±" indicates that the quadratic equation has two solutions.One learns about the "factor theorem," typically in a second course on algebra, as a way to find all roots that are rational numbers. One also learns how to find roots of all quadratic polynomials, using square roots (arising from the discriminant) when necessary. There are more advanced formulas for expressing roots of cubic and quartic polynomials, and also a number of numeric methods for approximating roots of arbitrary polynomials. These use methods from complex analysis as well as sophisticated numerical algorithms, and indeed, this is an area of ongoing research and development.

For equation solving, Wolfram|Alpha calls the Wolfram Language's Solve and Reduce functions, which contain a broad range of methods for all kinds of algebra, from basic linear and quadratic equations to multivariate nonlinear systems. In some cases, linear algebra methods such as Gaussian elimination are used, with optimizations to increase speed and reliability. Other operations rely on theorems and algorithms from number theory, abstract algebra and other advanced fields to compute results. These methods are carefully designed and chosen to enable Wolfram|Alpha to solve the greatest variety of problems while also minimizing computation time. While every effort is made to ensure that the content of this website and results returned by this tool are accurate, the website is provided on an “AS IS” basis and iChrome Ltd makes no representations or warranties in relation to the accuracy or completeness of the information. While the content of this site is provided in good faith, we do not warrant that the information will be kept up to date, be true, accurate and not misleading, or that this site will be available in the future. Nothing on this website should be taken to constitute professional advice or a formal recommendation and iChrome Ltd hereby excludes all representations and warranties whatsoever (whether implied by law or otherwise) relating to the content and use of this site. (Source: ichrome.com)

 

 

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