Quadratic Formula?

Question

How did the quadratic formula come about? (history)

Answer 1

On clay tablets dated between 1800 BC and 1600 BC, the ancient Babylonians left the earliest evidence of the discovery of quadratic equations, and also gave early methods for solving them. Indian mathematician Baudhayana who wrote a Sulba Sutra in ancient India circa 8th century BC first used quadratic equations of the form ax2 = c and ax2 + bx = c and also gave methods for solving them.

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, a Greek mathematician, produced a more abstract geometrical method around 300 BC. The Bakshali Manuscript written in India between 200 BC and 400 AD introduced the general algebraic formula for solving quadratic equations, and also introduced quadratic indeterminate equations (origin of type ax/c = y).

The first mathematician to have found negative solutions with the general algebraic formula was Brahmagupta (India, 7th century). Muḥammad ibn Mūsā al-Ḵwārizmī (Persia, 9th century) developed a set of formulae that worked for positive solutions. Turkish mathematician ibn Turk was one of the great minds of his time about quadratic equations. Abraham bar Hiyya Ha-Nasi (also known by the Latin name Savasorda) introduced the complete solution to Europe in his book Liber embadorum in the 12th century. Bhaskara II (1114-1185), an Indian mathematician-astronomer, also known as Bhaskara II and Bhaskara Achārya ("Bhaskara the teacher") solved quadratic equations with more than one unknown and is considered the originator of the equation.[2]

Shridhara (India, 9th century) was one of the first mathematicians to give a general rule for solving a quadratic equation. His original work is lost but Bhaskara II later quotes Shridhara's rule:

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.[3]

Answer 2

Quadratic Formula History

www.bbc.co.uk/dna/h2g2/A2982567 - 56k

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Answer 3

It came about largely out of intellectual competition...as also did the cubic formula.

Answer 4

Quadradious figured it out in around 20^2AD.

Answer 5

http://en.wikipedia.org/wiki/Quadratic_formula#History
http://www.bbc.co.uk/dna/h2g2/A2982567
It's interesting how far it goes back! Good question!