This document provides biographical and technical information about the Indian mathematician Sridharacharya. It notes that he lived in India in the 10th century AD and wrote two major treatises on mathematics. One of Sridharacharya's most important contributions was being one of the first to provide a formula for solving quadratic equations. The document examines his formula in detail and provides a proof of how it derives the two solutions to a quadratic equation.

1. Mathematics
Assignment
-Rachel Elizabeth
X-B
Roll no. 23

2. Sridharacharya

3. Sridhar Acharya (c. 870, India – c.
930 India) was
an Indian mathematician, Sanskrit pandit
and philosopher. He was born in
Bhurishresti (Bhurisristi or Bhurshut)
village in South Radha (at present Hughli)
in the 10th Century AD. His father's name
was Baladev Acharya and mother's name
was Acchoka. His father was also a
Sanskrit pandit.

4. Works:
• 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, interestcalculation, joint business or partnership and mensuration.
• He gave an exposition on zero. He has written, "If 0(zero) is
added to any number,the sum is the same number; If 0(zero)
is subtracted from any number,the number remains
unchanged; If 0(zero) is multiplied by any number,the product
is 0(zero)". He has said nothing about division of any number
by 0(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 practical applications
of algebra separated algebra from arithmetic
• He was one of the first to give a formula for solving quadratic
equations.

5. Biography:
• Sridhara is now believed to have lived in the ninth and tenth
centuries. However, there has been much dispute over his date
and in different works the dates of the life of Sridhara have been
placed from the seventh century to the eleventh century. The
best present estimate is that he wrote around 900 AD, a date
which is deduced from seeing which other pieces of mathematics
he was familiar with and also seeing which later mathematicians
were familiar with his work. Some historians give Bengal as the
place of his birth while other historians believe that Sridhara was
born in southern India.
• Sridhara is known as the author of two mathematical treatises,
namely the Trisatika (sometimes called the Patiganitasara ) and
the Patiganita. However at least three other works have been
attributed to him, namely the Bijaganita, Navasati, and Brhatpati.
Information about these books was given the works of Bhaskara
II (writing around 1150), Makkibhatta (writing in 1377), and
Raghavabhatta (writing in 1493).
• K.S. Shukla examined Sridhara's method for finding rational
solutions of , , , which Sridhara gives in the Patiganita. Shukla
states that the rules given there are different from those given by
other Hindu mathematicians.

6. • Sridhara was one of the first mathematicians to give a
rule to solve a quadratic equation. Unfortunately, as
indicated above, the original is lost and we have to rely
on a quotation of Sridhara's rule from Bhaskara II:• 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.

7. Proof of the Sridhar Acharya Formula:
• let us consider,
• Multipling both sides by 4a,
• Substracting from both sides,
• Then adding to both sides,
• We know that,
• Using it in the equation,

8. • Taking square roots,
• Hence, dividing by
get
• In this way, he found the proof of 2 roots.