Quadratic equation

In mathematics, a quadratic equation is a polynomial equation of the second degree. The generalized form is

History

The ancient Babylonians (around 400 BC) and Chinese used the method of completing the square to solve quadratic equations with positive roots, but did not have a general formula. Euclid produced a more abstract geometrical method around 300 BC.

Related Topics:
Babylonia - Chinese - Euclid

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The first mathematician known to have used the general algebraic formula, allowing negative as well as positive solutions, was Brahmagupta (India, 7th century). Al-Khwarizmi (Arabia, 11th century) independently developed a set of formulae that worked for positive solutions. Abraham bar Hiyya Ha-Nasi (also known by the Latin name Savasorda) was the first to introduce the complete solution to Europe in his book Liber embadorum.

Related Topics:
Brahmagupta - India - 7th century - Al-Khwarizmi - Arabia - 11th century - Abraham bar Hiyya Ha-Nasi - Latin - Savasorda

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Shridhara was said to be one of the first mathematicians to give a general rule for solving a quadratic equation. But there has been a dispute over his time. The rule is (as quoted by Bhaskara II):

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Multiply both sides of the equation by a known quantity equal to four times the coefficient of the square of the unknown; add to both sides a known quantity equal to the square of the coefficient of the unknown; then take the square root.http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Sridhara.html

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