Description
Polynomials (definition and examples), Euclid’s algorithm, synthetic division, common divisors, G.C.D. of polynomials. Roots of a polynomial equation, repeated roots and their multiplicity, common roots. Fundamental theorem of Algebra, Factor theorem, Complex roots of real polynomials occur in conjugate pairs with same multiplicity. Irrational roots of polynomials over rationals occur in conjugate pairs with same multiplicity.
Relation between roots and coefficients, Vieta’s formulae, symmetric functions, diminishing roots of a polynomial equation by h and its application, solution of a cubic when its roots are in A.P./G.P., solution of a biquadratic when its roots are in A.P. (respect. in G.P.) and sum (resp. product) of two roots is given, Descartes’Rule of Signs, Newton’s method of divisors for integral roots.
Transformation of equations: Transform the given polynomial equation into another such that signs of the roots changed, roots multiplied by a constant, roots are symmetric functions of the roots of the original equation. Solutions of cubic and bi-quadratic equations when their roots are in H.P.
Cardan’s method and trigonometric methods for solving cubic equations. Discriminant and nature of roots, of a real cubic equation. Descartes’ and Ferrari’s method of solving a bi-quadratic equation.
