Earliest method used to solve quadratic equation

Earliest Methods used to solve Quadratic Equation 1. Babylonian mathematics also known as Assyro-Babylonian mathematics was any mathematics developed or practiced by the people of Mesopotamia, from the days of the early Sumerians to the fall of Babylon in BC. Babylonian mathematical texts are plentiful and well edited.

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Earliest method used to solve quadratic equation

The numbers a , b , and c are the coefficients of the equation and may be distinguished by respectively calling them, the quadratic coefficient , the linear coefficient and the constant coefficient or free term. The values of x that satisfy the equation are called solutions of the equation, and roots or zeros of the expression on its left-hand side. A quadratic equation has at most two solutions. If there is only one solution, one says that it is a double root. If all the coefficients are real numbers , there are either two real solutions, or a single real double root, or two complex solutions that are complex conjugates of each other. A quadratic equation always has two roots, if complex roots are included; and a double root is counted for two. Completing the square is one of several ways for deriving the formula. Solutions to problems that can be expressed in terms of quadratic equations were known as early as BC. Because the quadratic equation involves only one unknown, it is called " univariate ". The quadratic equation contains only powers of x that are non-negative integers, and therefore it is a polynomial equation. In particular, it is a second-degree polynomial equation, since the greatest power is two. A quadratic equation with real or complex coefficients has two solutions, called roots. These two solutions may or may not be distinct, and they may or may not be real. In some cases, it is possible, by simple inspection, to determine values of p , q , r, and s that make the two forms equivalent to one another. Solving these two linear equations provides the roots of the quadratic.

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Quadratic, cubic and quartic equations. It is often claimed that the Babylonians about BC were the first to solve quadratic equations. This is an over simplification, for the Babylonians had no notion of 'equation'. What they did develop was an algorithmic approach to solving problems which, in our terminology, would give rise to a quadratic equation. The method is essentially one of completing the square. However all Babylonian problems had answers which were positive more accurately unsigned quantities since the usual answer was a length.

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Earliest method used to solve quadratic equation

The term "quadratic" comes from the Latin word "quadratus" meaning square, which refers to the fact that the variable x is squared in the equation. Did you know that when a rocket is launched, its path is described by a quadratic equation? Further, a quadratic equation has numerous applications in physics, engineering, astronomy, etc. Quadratic equations have maximum of two solutions, which can be real or complex numbers.

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With a purely geometric approach Pythagoras and Euclid created a general procedure to find solutions of the quadratic equation. There has been debate over the earliest appearance of Babylonian mathematics, with historians suggesting a range of dates between the 5th and 3rd millennia BC. In this context, the quadratic formula is not completely stable. If linear problems are found in their texts then the answers are simply given without any working; these problems were obviously thought too. History of Mathematics. It is hardly surprising then to find that the Babylonians were also proficient at solving quadratic equations. It is amazing that without the use of modern notation for these equations the Babylonians could recognise equations of a certain type and the methods for solving them. This article is about algebraic equations of degree two and their solutions. There is evidence dating this algorithm as far back as the Third Dynasty of Ur. If all the coefficients are real numbers , there are either two real solutions, or a single real double root, or two complex solutions that are complex conjugates of each other. In the quadratic formula, the expression underneath the square root sign is called the discriminant of the quadratic equation, and is often represented using an upper case D or an upper case Greek delta : [13]. Kabihasnang mesopotamia.

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Decent Essays. P Schultz,Tartaglia, Archimedes and cubic equations, Austral. The Greek mathematician Euclid circa BC used geometric methods to solve quadratic equations in Book 2 of his Elements , an influential mathematical treatise. Wikimedia Commons Wikibooks. Deepen heograpiyang pantao. These two solutions may or may not be distinct, and they may or may not be real. Retrieved 1 October Kabihasnang mesopotamia Nitz Antiniolos. Another great ruler was King Hammurabi of Babylon. Although these roots cannot be visualized on the graph, their real and imaginary parts can be. In his work, al-Khwarizmi explains the principles of solving linear and quadratic equations, the concept that an equation can be created to find the value of an unknown variable.