Sridharacharya: Solving Quadratic equations in the 9th Century.

Quadratic Equations and Roots

Sridhar Acharya (c. 870, India — c. 930 India) was an Indian mathematician, Sanskrit pundit and philosopher. He was born in Bhurishresti (Bhurisristi or Bhurshut) village in South Radha (at present Hughli) in the 10th Century AD.

He was known for two treatises: Trisatika(sometimes called the Patiganitasara) and the Patiganita. His major work Patiganitasara was named Trisatika because it was written in three hundred slokas. The book discusses counting of numbers, measures, natural number, multiplication, division, zero, squares, cubes, fraction, rule of three, interest-calculation, joint business or partnership and mensuration (the part of geometry concerned with ascertaining lengths, areas, and volumes).

He was one of the first to give a formula for solving quadratic equations. He discovered the formula :-

(Multiply by 4a)

Proof of the Sridhar Acharya Formula,

let us consider,
Multiplying both sides by 4a,
Substracting
from both sides,
Then adding
to both sides,
Using it in the equation,
Hence, dividing by
get

In this way, he found the proof of 2 roots.(http://en.m.wikipedia.org/wiki/Sridhara)

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