Quadratic formula (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Quadratic formula" in English language version.

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Starting from a quadratic equation of the form ⁠ $\textstyle ax^{2}+bx=c$ ⁠, Śrīdhara's method, as quoted by Bhāskara II (c. 1150): "Multiply both sides of the equation by a number equal to four times the [coefficient of the] square, and add to them a number equal to the square of the original [coefficient of the] unknown quantity. [Then extract the root.]".
Smith 1923, p. 446 Smith, David Eugene (1923), History of Mathematics, vol. 2, Boston: Ginn
Forsythe, George E. (1969), "Solving a Quadratic Equation on a Computer", The Mathematical Sciences: A Collection of Essays, MIT Press, pp. 138–152, ISBN 0-262-03026-8
Smith 1923, p. 380. Smith, David Eugene (1923), History of Mathematics, vol. 2, Boston: Ginn
Smith 1923, p. 134. Smith, David Eugene (1923), History of Mathematics, vol. 2, Boston: Ginn
Rene Descartes, The Geometry

archives-ouvertes.fr

hal.archives-ouvertes.fr

Goualard, Frédéric (2023), The Ins and Outs of Solving Quadratic Equations with Floating-Point Arithmetic (Technical report), University of Nantes, HAL hal-04116310

books.google.com

Sterling, Mary Jane (2010), Algebra I For Dummies, Wiley Publishing, p. 219, ISBN 978-0-470-55964-2
Rich, Barnett; Schmidt, Philip (2004), Schaum's Outline of Theory and Problems of Elementary Algebra, The McGraw–Hill Companies, Chapter 13 §4.4, p. 291, ISBN 0-07-141083-X
Prasolov, Viktor; Solovyev, Yuri (1997), Elliptic functions and elliptic integrals, AMS Bookstore, p. 134, ISBN 978-0-8218-0587-9
Irving 2013, p. 34. Irving, Ron (2013), Beyond the Quadratic Formula, MAA, ISBN 978-0-88385-783-0
The Cambridge Ancient History Part 2 Early History of the Middle East, Cambridge University Press, 1971, p. 530, ISBN 978-0-521-07791-0
Irving 2013, p. 39. Irving, Ron (2013), Beyond the Quadratic Formula, MAA, ISBN 978-0-88385-783-0
Irving 2013, p. 42. Irving, Ron (2013), Beyond the Quadratic Formula, MAA, ISBN 978-0-88385-783-0

csusm.edu

public.csusm.edu

Aitken, Wayne, "A Chinese Classic: The Nine Chapters" (PDF), Mathematics Department, California State University, retrieved 28 April 2013

doi.org

Specifically, Fagnano began with the equation ⁠ $xx+bb=ax$ ⁠ and found the solutions to be $x={\frac {2bb}{a\mp a{\sqrt {1-{\dfrac {4bb}{aa}}}}}}.$ (In the 18th century, the square ⁠ $\textstyle x^{2}$ ⁠ was conventionally written as ⁠ $xx$ ⁠.)

Fagnano, Giulio Carlo (1750), "Applicazione dell' algoritmo nuovo Alla resoluzione analitica dell' equazioni del secondo, del terzo, e del quarto grado" [Application of a new algorithm to the analytical resolution of equations of the second, third, and fourth degree], Produzioni matematiche del conte Giulio Carlo di Fagnano, Marchese de' Toschi, e DiSant' Ononio (in Italian), vol. 1, Pesaro: Gavelliana, Appendice seconda, eq. 6, p. 467, doi:10.3931/e-rara-8663
Hoehn, Larry (1975), "A More Elegant Method of Deriving the Quadratic Formula", The Mathematics Teacher, 68 (5): 442–443, doi:10.5951/MT.68.5.0442, JSTOR 27960212
Debnath, Lokenath (2009), "The legacy of Leonhard Euler – a tricentennial tribute", International Journal of Mathematical Education in Science and Technology, 40 (3): 353–388, doi:10.1080/00207390802642237, S2CID 123048345
Thompson, H. Bradford (1987), "Good numerical technique in chemistry: The quadratic equation", Journal of Chemical Education, 64 (12): 1009, doi:10.1021/ed064p1009
Baker, Henry G. (1998), "You Could Learn a Lot from a Quadratic: Overloading Considered Harmful", SIGPLAN Notices, 33 (1): 30–38, doi:10.1145/609742.609746

dtic.mil

apps.dtic.mil

Forsythe, George E. (1966), How Do You Solve a Quadratic Equation (PDF) (Tech report), Stanford University, STAN-CS-66-40 (AD639052)

ethz.ch

era-prod11.ethz.ch

Specifically, Fagnano began with the equation ⁠ $xx+bb=ax$ ⁠ and found the solutions to be $x={\frac {2bb}{a\mp a{\sqrt {1-{\dfrac {4bb}{aa}}}}}}.$ (In the 18th century, the square ⁠ $\textstyle x^{2}$ ⁠ was conventionally written as ⁠ $xx$ ⁠.)

Fagnano, Giulio Carlo (1750), "Applicazione dell' algoritmo nuovo Alla resoluzione analitica dell' equazioni del secondo, del terzo, e del quarto grado" [Application of a new algorithm to the analytical resolution of equations of the second, third, and fourth degree], Produzioni matematiche del conte Giulio Carlo di Fagnano, Marchese de' Toschi, e DiSant' Ononio (in Italian), vol. 1, Pesaro: Gavelliana, Appendice seconda, eq. 6, p. 467, doi:10.3931/e-rara-8663

jstor.org

Goff, Gerald K. (1976), "The Citardauq Formula", The Mathematics Teacher, 69 (7): 550–551, JSTOR 27960584
Hoehn, Larry (1975), "A More Elegant Method of Deriving the Quadratic Formula", The Mathematics Teacher, 68 (5): 442–443, doi:10.5951/MT.68.5.0442, JSTOR 27960212

kent.edu

etna.math.kent.edu

Mastronardi, Nicola; Van Dooren, Paul (2015), "Revisiting the stability of computing the roots of a quadratic polynomial", Electronic Transactions on Numerical Analysis, 44: 73–83

khanacademy.org

"Discriminant review", Khan Academy, retrieved 2019-11-10
"Understanding the quadratic formula", Khan Academy, retrieved 2019-11-10

knaw.nl

dwc.knaw.nl

Struik, D. J.; Stevin, Simon (1958), The Principal Works of Simon Stevin, Mathematics (PDF), vol. II–B, C. V. Swets & Zeitlinger, p. 470

mathwarehouse.com

"Axis of Symmetry of a Parabola. How to find axis from equation or from a graph. To find the axis of symmetry ...", www.mathwarehouse.com, retrieved 2019-11-10

semanticscholar.org

api.semanticscholar.org

Debnath, Lokenath (2009), "The legacy of Leonhard Euler – a tricentennial tribute", International Journal of Mathematical Education in Science and Technology, 40 (3): 353–388, doi:10.1080/00207390802642237, S2CID 123048345

st-andrews.ac.uk

mathshistory.st-andrews.ac.uk

O'Connor, John J.; Robertson, Edmund F. (2000), "Sridhara", MacTutor History of Mathematics Archive, University of St Andrews