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MTH-202 | Theory of Equations

F.Y.B.Sc. | Sem II | Mathematics

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F.Y.B.Sc. | Sem II | MTH-202
Theory of Equations

We feel great pleasure in bringing out this books. The book has been written according to revised syllabus of KBC North Maharashtra University, Jalgaon for F.Y.B.Sc. Mathematics, MTH – 202 – Theory of Equations which is implemented form June 2022 (CBCS Pattern).
Each topic has been written in a very simple and lucid language to enable the students to understand the subject thoroughly. There are many worked examples with detailed steps. The problems in the exercises have been complied taking into consideration the academic background of students. We hope that the text will be equally appreciated by the students and the teachers.

Unit 1 Divisibility of Integers
1.1 Natural Numbers
1.2 Peano’s Axioms
1.3 Well Ordering Principle
1.4 Principle of Mathematical Induction
1.5 Divisibility
1.6 Division Algorithm
1.7 Greatest Common Divisor
1.8 Least Common Multiple
1.9 Euclidean Algorithm
1.10 Prime and Composite Numbers
1.11 Unique Factorization Theorem

Unit 2 Polynomials
2.1 Polynomial
2.2 Horner’s Method of Synthetic Division
2.3 Greatest Common Divisor of Polynomials
2.4 Fundamental Theorem of Algebra
2.5 Method to Find Common Roots of Polynomial Equation
2.6 Descarte’s Rule of Signs
2.7 Newton’s Method of Divisors for the Integral Roots

Unit 3 Theory of Equations – I
3.1 Relation between the roots and coefficients of general polynomial equation
3.2 Relation between the roots and coefficients of quadratic, cubic and biquadratic equation
3.3 Symmetric functions of the roots

Unit 4 Theory of Equations – II
4.1 Transformation of Equations
4.2 Carden’s Method of solving the cubic equation
4.3 Descarte’s method of solving biquadratic equations


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