Sridhara's Contributions to Algebra

Description: Sridhara's Contributions to Algebra
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Who is known as the first Indian mathematician to provide a systematic study of indeterminate equations of the first degree?

  1. Aryabhata

  2. Bhaskara II

  3. Sridhara

  4. Brahmagupta


Correct Option: C
Explanation:

Sridhara was the first Indian mathematician to provide a systematic study of indeterminate equations of the first degree.

What is the name of the method developed by Sridhara for solving indeterminate equations of the first degree?

  1. Kuttaka method

  2. Chakravala method

  3. Bhaskara's method

  4. Aryabhata's method


Correct Option: A
Explanation:

The Kuttaka method is a method developed by Sridhara for solving indeterminate equations of the first degree.

What is the main idea behind the Kuttaka method?

  1. Using continued fractions

  2. Using the Euclidean algorithm

  3. Using the method of false position

  4. Using the method of exhaustion


Correct Option: A
Explanation:

The main idea behind the Kuttaka method is to use continued fractions to find a solution to the indeterminate equation.

What is the general form of an indeterminate equation of the first degree?

  1. $ax + by = c$

  2. $ax^2 + bx + c = 0$

  3. $ax^3 + bx^2 + cx + d = 0$

  4. $ax^4 + bx^3 + cx^2 + dx + e = 0$


Correct Option: A
Explanation:

The general form of an indeterminate equation of the first degree is $ax + by = c$, where $a$, $b$, and $c$ are integers and $x$ and $y$ are the unknowns.

What is the significance of Sridhara's work on indeterminate equations?

  1. It led to the development of new methods for solving linear equations.

  2. It provided a foundation for the study of number theory.

  3. It influenced the work of later mathematicians such as Bhaskara II.

  4. All of the above


Correct Option: D
Explanation:

Sridhara's work on indeterminate equations had a significant impact on the development of mathematics. It led to the development of new methods for solving linear equations, provided a foundation for the study of number theory, and influenced the work of later mathematicians such as Bhaskara II.

What other contributions did Sridhara make to algebra?

  1. He developed a method for solving quadratic equations.

  2. He developed a method for solving cubic equations.

  3. He developed a method for solving quartic equations.

  4. He developed a method for solving quintic equations.


Correct Option: A
Explanation:

In addition to his work on indeterminate equations, Sridhara also developed a method for solving quadratic equations.

What is the name of the method developed by Sridhara for solving quadratic equations?

  1. Kuttaka method

  2. Chakravala method

  3. Bhaskara's method

  4. Aryabhata's method


Correct Option: B
Explanation:

The Chakravala method is a method developed by Sridhara for solving quadratic equations.

What is the main idea behind the Chakravala method?

  1. Using continued fractions

  2. Using the Euclidean algorithm

  3. Using the method of false position

  4. Using the method of exhaustion


Correct Option: C
Explanation:

The main idea behind the Chakravala method is to use the method of false position to find a solution to the quadratic equation.

What is the significance of Sridhara's work on quadratic equations?

  1. It led to the development of new methods for solving quadratic equations.

  2. It provided a foundation for the study of algebra.

  3. It influenced the work of later mathematicians such as Bhaskara II.

  4. All of the above


Correct Option: D
Explanation:

Sridhara's work on quadratic equations had a significant impact on the development of mathematics. It led to the development of new methods for solving quadratic equations, provided a foundation for the study of algebra, and influenced the work of later mathematicians such as Bhaskara II.

What other contributions did Sridhara make to mathematics?

  1. He developed a method for solving cubic equations.

  2. He developed a method for solving quartic equations.

  3. He developed a method for solving quintic equations.

  4. He developed a method for solving sextic equations.


Correct Option: A
Explanation:

In addition to his work on indeterminate equations and quadratic equations, Sridhara also developed a method for solving cubic equations.

What is the name of the method developed by Sridhara for solving cubic equations?

  1. Kuttaka method

  2. Chakravala method

  3. Bhaskara's method

  4. Aryabhata's method


Correct Option: C
Explanation:

The Bhaskara's method is a method developed by Sridhara for solving cubic equations.

What is the main idea behind the Bhaskara's method?

  1. Using continued fractions

  2. Using the Euclidean algorithm

  3. Using the method of false position

  4. Using the method of exhaustion


Correct Option: D
Explanation:

The main idea behind the Bhaskara's method is to use the method of exhaustion to find a solution to the cubic equation.

What is the significance of Sridhara's work on cubic equations?

  1. It led to the development of new methods for solving cubic equations.

  2. It provided a foundation for the study of algebra.

  3. It influenced the work of later mathematicians such as Bhaskara II.

  4. All of the above


Correct Option: D
Explanation:

Sridhara's work on cubic equations had a significant impact on the development of mathematics. It led to the development of new methods for solving cubic equations, provided a foundation for the study of algebra, and influenced the work of later mathematicians such as Bhaskara II.

What other contributions did Sridhara make to mathematics?

  1. He developed a method for solving quartic equations.

  2. He developed a method for solving quintic equations.

  3. He developed a method for solving sextic equations.

  4. He developed a method for solving septic equations.


Correct Option: A
Explanation:

In addition to his work on indeterminate equations, quadratic equations, and cubic equations, Sridhara also developed a method for solving quartic equations.

What is the name of the method developed by Sridhara for solving quartic equations?

  1. Kuttaka method

  2. Chakravala method

  3. Bhaskara's method

  4. Aryabhata's method


Correct Option: D
Explanation:

The Aryabhata's method is a method developed by Sridhara for solving quartic equations.

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