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Mathematics in Ancient and Medieval India c7.s1: Quadratic Equation

Mathematics in Ancient and Medieval India c7.s1

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Quadratic Equation

c7.s1.1

The *Śulbasūtras* contain problems involving quadratic equations of the type : ax² = c, ax² + bx = c but give no solution. The *Bakhshālī Ms.* gives the solution of a problem in the form which reduces to $x = (√(b² - 4ac) - b)/2a$

c7.s1.2

Āryabhaṭa I (499 A. D.) and Brahmagupta (628 A. D.) clearly indicate their knowledge of quadratic equations and their solutions. In connection with an interest prob'em, Āryabhaṭa I gave the solution which in symbo s runs as follows : $x = (-p + √(p² + 4tpq))/2t$ where p = principal, t = time, q = sum of interest on principal and interest on interest in time t; x = interest on principal in unit time.

c7.s1.3

A similar quadratic solution arising out of an interest problem is given by Brahmagupta. He has also given a solution of the problem of quadratic equations in connection with the determination of the number of terms (n) in an A. P.

c7.s1.4

The method of transforming the left hand side of the quadratic equation ax² + bx = c into a whole square by multiplying both sides by 4a, adding b² and taking the square root, is given by Śrīdhara (c. 991 A.D.) in his algebra which is lost but preserved in the quotations of Bhāskara II (c. 1150 A. D. ), Jñānarāja and Sūryadāsa. Datta and Singh discussed in detail all these Indian methods of solving the quadratic equation in their work, *History of Hindu Mathematics*.¹

c7.s1.5

¹ Datta, B. and *Singh, A. N. History of Hindu Mathematics*, 2, p. 59-87, Lahore, 1938.

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