Who invented the quadratic formula wikipedia

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Related titles. Carousel Previous Carousel Next. Jump to Page. Search inside document. The general quadratic equation is Here x represents an unknown, while a, b, and c are constants with a not equal to 0. By substitution Another technique is solution by substitution. One can recover the roots from the resolvents by inverting the above equations: Thus, solving for the resolvents gives the original roots. By extrema Knowing the value of x in the functional extreme point makes it possible to solve only for the increase or decrease needed in x to solve the quadratic equation.

See also Discriminant Fundamental theorem of algebra References 1. Gary Cousin. Amrutham Suresh. Becky May Sajo. Mariel Pastolero. Allan Gulinao. Saahil Ledwani. Ashok Bharti. Island Boy. Arihant Kumar. Keri-ann Millar. Marites Balmas. Graham Moore. Information about these books was given the works of Bhaskara II writing around , Makkibhatta writing in , and Raghavabhatta writing in We give details below of Sridhara's rule for solving quadratic equations as given by Bhaskara II. There is another mathematical treatise Ganitapancavimsi which some historians believe was written by Sridhara.

Hayashi in [ 7 ] , however, argues that Sridhara is unlikely to have been the author of this work in its present form. The Patiganita is written in verse form. The book begins by giving tables of monetary and metrological units. Following this algorithms are given for carrying out the elementary arithmetical operations, squaring, cubing, and square and cube root extraction, carried out with natural numbers. Through the whole book Sridhara gives methods to solve problems in terse rules in verse form which was the typical style of Indian texts at this time.

All the algorithms to carry out arithmetical operations are presented in this way and no proofs are given.

Indeed there is no suggestion that Sridhara realised that proofs are in any way necessary. To top. English American Examples Translations. Sign up for free and get access to exclusive content:. Free word lists and quizzes from Cambridge. Tools to create your own word lists and quizzes.

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Higher degree polynomial equations can be very difficult to solve. In some special situations, however, they can be made more manageable by reducing their exponents via substitution. If a substitution can be made such that the higher order polynomial takes the form of a quadratic, any method for solving a quadratic equation can be applied. For example, if a quartic equation is biquadratic—that is, it includes no terms of an odd-degree— there is a quick way to find the zeroes of the quartic function by reducing it into a quadratic form.

Consider a quadratic function with no odd-degree terms which has the form:. With substitution, we were able to reduce a higher order polynomial into a quadratic equation. It can now be solved with any of a number of methods via graphing, factoring, completing the square, or by using the quadratic formula. It is important to realize that the same kind of substitution can be done for any equation in quadratic form, not just quartics.

A similar procedure can be used to solve higher-order equations. Privacy Policy. Skip to main content.