Sridhara

Sridharacharya (Bengali: শ্রীধর আচার্য; c. 750 CE – c. 930 CE) was an Indian mathematician, Sanskrit pandit and philosopher. He was born in Bhurishresti (Bhurisristi or Bhurshut) village in South Radha (at present day Hughli) in the 8th Century AD. His father's name was Baladev Acharya and his mother's name was Acchoka bai. His father was a Sanskrit pandit and philosopher.

He gave an exposition on the zero. He wrote, "If zero is added to any number, the sum is the same number; if zero is subtracted from any number, the number remains unchanged; if zero is multiplied by any number, the product is zero".
In the case of dividing a fraction he has found out the method of multiplying the fraction by the reciprocal of the divisor.
He wrote on the practical applications of algebra
He separated algebra from arithmetic
He was one of the first to give a formula for solving quadratic equations.

Derivation:

ax^{2}+bx+c=0

Multiply both sides by 4a,

4a^{2}x^{2}+4abx+4ac=0

Subtract 4ac from both sides,

4a^{2}x^{2}+4abx=-4ac

Add

b^{2}

to both sides,

4a^{2}x^{2}+4abx+b^{2}=-4ac+b^{2}

Since

(m+n)^{2}=m^{2}+2mn+n^{2}

Complete the square on the left side,

(2ax+b)^{2}=b^{2}-4ac={D}

Take square roots,

2ax+b=\pm {\sqrt {D}}

2ax=-b\pm {\sqrt {D}}

and, divide by 2a,

x={\frac {-b\pm {\sqrt {b^{2}-4ac\ }}}{2a}}.

Bibliography

O'Connor, John J.; Robertson, Edmund F., "Sridhara", MacTutor History of Mathematics archive, University of St Andrews .
The Date of Sridharacharya by S. Srikanta Sastri, The Jaina Antiquary (Jan, 1948)

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