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State the following statement is true or false.
Indian mathematicians like Aryabhatt, Brahmagupta, Mahavira, Shridhar have contributed to the field of algebra.
A. TRUE
B. FALSE

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Last updated date: 20th Jun 2024
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Answer
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Hint: Here we will check for each mathematician Aryabhatt, Brahmagupta, Mahavira, Shridhar and check if they all worked on the field of algebra. We must check the contributions of each of the mathematicians and then check their contributions in Algebra.

Complete step-by-step answer:
We write the concepts each mathematician wrote about in the field of algebra.
* Aryabhatt or Aryabahta was first of the mathematicians and astronomers from the classic age of Indian mathematics. He wrote Aryabhatiya in 499CE when he was 23 years old. The Aryabhatiya mentioned about algebra as he provided results for summation of series of squares and cubes as \[{1^2} + {2^2} + ..... + {n^2} = \dfrac{{n(n + 1)}}{2}\] and \[{1^3} + {2^3} + ......{n^3} = {(1 + 2 + .....n)^2}\]. He gave methods of addition, subtraction multiplication of simple and compound algebraic equations.
* Brahmagupta was a mathematician and astronomer who wrote Brahmasphutasiddhanta in 628CE. He gave the solution of a general linear equation in Brahmasphutasiddhanta stating that a quadratic equation \[a{x^2} + bx = c\]has solutions \[x = \dfrac{{ \pm \sqrt {4ac + {b^2}} - b}}{{2a}}\] and \[x = \dfrac{{\sqrt {ac + \dfrac{{{b^2}}}{4}} - \dfrac{b}{2}}}{a}\]
* Mahavira was a mathematician of the ninth century who wrote Ganita Sara Sangraha in which he focused on techniques which are necessary to solve algebraic equations, he gave formula for area and perimeter of ellipse and found methods to find square and cube root of a number. He also gave the point that the square root of a negative number doesn’t exist.
* Shridhar was a mathematician and a philosopher who wrote Trisatika which is written in three hundred slokas around 900AD.He gave practical applications of algebra and separated algebra from arithmetic. Also, he was the first person to give roots of quadratic equation by \[\dfrac{{ - b \pm \sqrt {{b^2} - 4ac} }}{{2a}}\] where the quadratic equation is \[a{x^2} + bx = c\].
From all these four works by four great mathematicians we can say they all wrote about the field of algebra. So the statement given in the question is TRUE.
So, option A is correct.

Note: Students can easily get confused with repetition of work in field of algebra by several mathematician but they should keep in mind that mathematicians tried to improve the solutions and made the formulas as simpler as they could be, so there might be more than one mathematician having the same work in a field.