What is the history of the quadratic formula?

Answer 1

The Babylonians, as early as 1800 BC (displayed on Old Babylonian clay tablets) had an early version.

In the Sulba Sutras in ancient India circa 8th century BC quadratic equations of the form ax2 = c and ax2 + bx = c were explored using geometric methods. Babylonian mathematicians from circa 400 BC and Chinese mathematicians from circa 200 BC used the method of completing the square to solve quadratic equations with positive roots, but did not have a general formula. Euclid, the Greek mathematician, produced a more abstract geometrical method around 300 BC. In 628 CE, Brahmagupta, an Indian mathematician, gave the first explicit (although still not completely general) solution of the quadratic equation: " To the absolute number multiplied by four times the [coefficient of the] square, add the square of the [coefficient of the] middle term; the square root of the same, less the [coefficient of the] middle term, being divided by twice the [coefficient of the] square is the value. (Brahmasphutasiddhanta (Colebrook translation, 1817, page 346)[2] " The Bakhshali Manuscript dated to have been written in India in the 7th century CE contained an algebraic formula for solving quadratic equations, as well as quadratic indeterminate equations (originally of type ax/c = y). Mohammad bin Musa Al-kwarismi (Persia, 9th century) developed a set of formulas that worked for positive solutions based on Brahmagupta.[3] The Catalan Jewish mathematician Abraham bar Hiyya Ha-Nasi authored the first book to include the full solution to the general quadratic equation.[4] The writing of the Chinese mathematician Yang Hui (1238-1298 AD) represents the first in which quadratic equations with negative coefficients of 'x' appear, although he attributes this to the earlier Liu Yi. The first appearance of the general solution in the modern mathematical literature is evidently in an 1896 paper by Henry Heaton.[5] # ^ Stillwell, p. 86. # ^ a bStillwell, p. 87. # ^ BBC - h2g2 - The History Behind The Quadratic Formula # ^ The Equation that Couldn't be Solved # ^ Heaton, H. (1896) A Method of Solving Quadratic Equations, American Mathematical Monthly 3(10), 236-237.