quadratic equation
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Mathematicians of Quadratic Equation The earliest solutions to quadratic equations involving an unknown are found in Babylonian mathematical texts that date back to about 2000 B.C. The ancient Babylonians (around 400 BC) used the method of completing the square to solve quadratic equations with positive roots, but did not have a general formula. At this time the Babylonians did not recognize negative or complex roots because all quadratic equations were employed in problems that had positive answers such as length. The theory involving quadratic equations, and all polynomial equations, was flawed prior to the 17th century because of this idea. In 400 B.C. the Babylonians developed the quadratic formula used to find the roots of quadratic equations. About 100 years later Euclid formulated a geometrical approach to solving quadratic equations. He produced a more abstract geometrical method. His approach involved determining a length that would be the root of a quadratic equation. There were many other methods used in ancient times to determine the roots to quadratic equations. The Egyptians employed the false position method which involved approximating x to make part of the quadratic equation easy to calculate. Then a scaling factor was incorporated to find the root of the original equation. In the 3rd century, the Greek mathematician Diophantus of Alexandria wrote his book Arithmetica. Of the 13 parts originally written, only six still survive, but they provide the earliest record of an attempt to use symbols to represent unknown quantities. Diophantus did not consider general methods in Arithmetica, but instead solved a large number of practical problems.Greek mathematicians employed the iteration method in which a positive root of a quadratic equation is approximated and substituted for the unknown. Then this is used to form another approximation that is substituted and calculated. This process is repeated until the real root is determined.
Several Indian mathematicians carried out important work in the field of algebra in the 6th and 7th centuries. These include Aryabhatta, whose book entitled Aryabhatta included work on linear and quadratic equations, and Brahmagupta, who presented a general solution for a quadratic equationThe first mathematician known to have used the general algebraic formula, allowing negative as well as positive solutions, was Brahmagupta (India, 7th century).He advanced the Babylonian methods to almost modern methods. Indian and Chinese mathematicians recognized negative roots to quadratic equations The next major development in the history of algebra was the book al-Kitab almuhtasar fi hisab al-jabr wa'l-muqabala ("Compendium on calculation by completion and balancing"), written by the Arabic mathematician Al-Khwarizmi in the 9th century. The word algebra is derived from al-jabr, or "completion". He developed a classification of quadratic equations in the 9th century. He independently developed a set of formulae that worked for positive solutions. They were classified into one of six different types depending on which coefficients were negative. He wrote six chapters with each chapter devoted to a different type of equation. The equations were composed to three types of quantities: roots, squares of roots and numbers, and numbers. The six chapters are : 1)Squares equal to roots. 2)Squares equal to numbers. 3)Roots equal to numbers. 4)Squares and roots equal to numbers, e.g. x2 + 10x = 39. 5)Squares and numbers equal to roots, e.g. x2 + 21 = 10x. 6)Roots and numbers equal to squares, e.g. 3x + 4 = x In each chapter al-Khwarizmi described the rule used for solving each type of quadratic equation and then presented a proof for each example.
Later, in 1145, Abraham bar Hiyya Ha-Nasi, also known by the Latin name Savasorda, published a book that was the first to give the complete solution of the quadratic equation. He was the first to introduce the complete solution to Europe in his book Liber embadorum. Over the next few hundred years several mathematicians advanced the study of quadratic and cubic equations. Near the end of the 18th century Carl Friedrich Gauss, a German mathematician, gave a proof that showed every polynomial equation has at least one root. The root may not be able to be expressed as an algebraic formula involving the coefficients of the equation but a root did exist. Eventually a team of three international mathematicians combined and showed that only polynomials of degree five or less could be solved via a general algebraic formula.It is this set of polynomials that the theory of equations focuses on.
Several Indian mathematicians carried out important work in the field of algebra in the 6th and 7th centuries. These include Aryabhatta, whose book entitled Aryabhatta included work on linear and quadratic equations, and Brahmagupta, who presented a general solution for a quadratic equationThe first mathematician known to have used the general algebraic formula, allowing negative as well as positive solutions, was Brahmagupta (India, 7th century).He advanced the Babylonian methods to almost modern methods. Indian and Chinese mathematicians recognized negative roots to quadratic equations The next major development in the history of algebra was the book al-Kitab almuhtasar fi hisab al-jabr wa'l-muqabala ("Compendium on calculation by completion and balancing"), written by the Arabic mathematician Al-Khwarizmi in the 9th century. The word algebra is derived from al-jabr, or "completion". He developed a classification of quadratic equations in the 9th century. He independently developed a set of formulae that worked for positive solutions. They were classified into one of six different types depending on which coefficients were negative. He wrote six chapters with each chapter devoted to a different type of equation. The equations were composed to three types of quantities: roots, squares of roots and numbers, and numbers. The six chapters are : 1)Squares equal to roots. 2)Squares equal to numbers. 3)Roots equal to numbers. 4)Squares and roots equal to numbers, e.g. x2 + 10x = 39. 5)Squares and numbers equal to roots, e.g. x2 + 21 = 10x. 6)Roots and numbers equal to squares, e.g. 3x + 4 = x In each chapter al-Khwarizmi described the rule used for solving each type of quadratic equation and then presented a proof for each example.
Later, in 1145, Abraham bar Hiyya Ha-Nasi, also known by the Latin name Savasorda, published a book that was the first to give the complete solution of the quadratic equation. He was the first to introduce the complete solution to Europe in his book Liber embadorum. Over the next few hundred years several mathematicians advanced the study of quadratic and cubic equations. Near the end of the 18th century Carl Friedrich Gauss, a German mathematician, gave a proof that showed every polynomial equation has at least one root. The root may not be able to be expressed as an algebraic formula involving the coefficients of the equation but a root did exist. Eventually a team of three international mathematicians combined and showed that only polynomials of degree five or less could be solved via a general algebraic formula.It is this set of polynomials that the theory of equations focuses on.
