Skip to main content

Shridharacharya: Solving Quadratic equations in the 9th Century.

Sridhar Acharya (c. 870, India – c. 930 India) was an Indian mathematician, Sanskrit pundit andphilosopher. 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 thePatiganita. 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 was one of the first to give a formula for solving quadratic equations.He found the formula :-

 (Multiply by 4a)

Proof of the Sridhar Acharya Formula,

let us consider,

ax^2 + bx + c = 0

  • Multipling both sides by 4a,

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

  • Substracting 4ac from both sides,

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

  • Then adding b^2 to both sides,

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

  • We know that,

(a + b)^2 = a^2 + 2ab + b^2

  • Using it in the equation,

(2ax + b)^2 = b^2 - 4ac

  • Taking square roots,

2ax + b = \pm\sqrt{b^2 - 4ac}

2ax = -b\pm\sqrt{b^2 - 4ac}

  • Hence, dividing by 2a get

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

In this way, he found the proof of 2 roots.(


Popular posts from this blog

What is OOP? In Layman terms...

What is OOP? OOP stands for Object Oriented Programming. It is not just a programming language, but a paradigm (An example or model used to explain a concept or theory). OOP does not tell you how to program, rather it tells you how to go about designing your software. There are many languages that implement/help you in implementing OOP. C++ is one of them. When you are developing Object-oriented programs/software the emphasis is more on how you think about and design the software rather that on actually implementing(coding) it. Why ‘Object-Oriented’?       What should you do to make sure your program is object oriented? Simple, you stop thinking in terms of Bits, Bytes, Pointers, unions, structures, et al. Instead you think in terms of objects and the interactions between them. It is actually more natural for humans to think Object-oriented than to think in terms of memory and variables, etc.       Simply put, OO is nothing but defining the behavior of software as a collecti…

BLACK...Hindi Cinema's Coming of Age Movie....

Went to See BLACK this Saturday with my Friends.... It was a really unforgettable Experience...BLACK is Unlike any HIndi Movie ever-made. It is Stark, Thought Provoking, Rough, Beautiful, Poetic, Gossamer, and Tough at the same time. Very Few Movie-Makers are able to attain this level of Movie Making. Hats off to Sanjay Leela Bhansali. Black stars Amitabh Bachchan and Rani Mukerji. Bacchan, in one of his best roles, plays the TEACHER and Portrays both Unsurmountable Weakness and Indomitable Strength with equal Ease. Rani(the Girl Next Door) portrays the role of a Deaf and Blind Girl with such conviction, that the viewer cannot help but get affected with her plight. Ayesha Kapur plays the young Rani -- a blind, deaf and hence mute girl -- to perfection. One can just wonder at the performance by a 10 year old little girl. Frustrated by her inability to comprehend the world around her, little Michelle McNally is an untamed 'animal'. Her Father keeps a distance, her mother is to…