Sridhara (RUDRA PROSAD GHOSH. ROLL- 19)

He contributed a lot in mathematics. He was known for 2 treatises: Trisatika (nitsometimes 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.

• 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:

${\displaystyle ax^{2}+bx+c=0}$

Multiply both sides by 4a,

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

Subtract 4ac from both sides,

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

Add ${\displaystyle b^{2}}$ to both sides,

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

Since

${\displaystyle (m+n)^{2}=m^{2}+2mn+n^{2}}$

Complete the square on the left side,

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

Take square roots,

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

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

and, divide by 2a,

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

a+b