A number of Indian mathematicians gave rules equivalent to the quadratic formula. It is possible that certain altar constructions dating from ca. 500 BC represent
solutions of the equation, but even should this be the case, there is no record of
the method of solution (Smith 1953, p. 444). The Hindu mathematician Āryabhata
(475 or 476-550) gave a rule for the sum of a geometric series that shows knowledge
of the quadratic equations with * both* solutions (Smith 1951, p. 159; Smith
1953, p. 444), while Brahmagupta (ca. 628) appears to have considered only one
of them (Smith 1951, p. 159; Smith 1953, pp. 444-445). Similarly, Mahāvīra
(ca. 850) had substantially the modern rule for the positive root of a quadratic.
Srīdhara (ca. 1025) gave the positive root of the quadratic formula, as stated
by Bhāskara (ca. 1150; Smith 1953, pp. 445-446). The Persian mathematicians
al-Khwārizmī (ca. 825) and Omar Khayyám (ca. 1100) also gave rules
for finding the positive root.