Title USOL_THEORY OF EQUATION (PAPER - III)_BA_BSc 2nd SEMESTER (P.U.).pdf ✅

Chairperson : Prof. Neeru Department Coordinator : Dr. Vinay Kanwar B.A. SEMESTER – II, MATHEMATICS PAPER : III, THEORY OF EQUATION CONTENTS L. No. Title Author Page No. 1. Polynomials Divisibility Prof. G. S. Sandhu 1 2. Roots and coefficients of Prof. G. S. Sandhu 35 Polynomial Equations 3. Rational and Real Roots of Prof. G. S. Sandhu 54 Polynomials 4. Solution of Cubic Equations Prof. G. S. Sandhu 67 Vetter : Dr. Vinay Kanwar E-Mail of Department - [email protected] Contact No. of Department - 0172-2534330


Paper III: THEORY OF EQUATIONS Max. Marks : 30 Time : 3 Hours Note: 1. The syllabus has been split into two Units: Unit-I and Unit-II. Four questions will be set from each Unit. 2. A student will be asked to attempt five questions selecting at least two questions from each Unit. Each question will carry 6 marks. 3. The teaching time shall be five periods (45 minutes each) per paper per week including tutorial. 4. If internal assessment is to be conducted in the form of written examinations, then there will be only one written examination in a Semester Unit-I Euclid’s algorithm, synthetic division, roots and their multiplicity. Complex roots of real polynomials occur inconjugate pairs with same multiplicity. Relation between roots and coefficients.Transformation of equations.Descartes’ Rule of Signs. Unit-II Newton’s method of divisors, Solution of cubic and bi-quadratic equations, Cardan’s method of solving acubic, discriminant and nature of roots of real cubic, trigonometric solutions of a real cubic with real roots. Descarte’s and Ferrari’s method for a bi- quadratic. References: 1. S.R. Knight and H.S. Hall : Higher Algebra, H. M. Publications, 1994. 2. Chandrika Prasad : Text Book on Algebra and Theory of Equations, Pothishala Private Ltd., Allahabad.