Euclid’s algorithm, Synthetic division, Roots and their multiplicity. Complex roots of real polynomials occur in conjugate pairs with same multiplicity. Relation between roots and coefficients. Transformation of equations. Descartes’ Rule of Signs.
Newton’s method of divisors, Solution of cubic and bi-quadratic equations, Cardon’s method of solving a cubic, Discriminant and nature of roots of real cubic, Trigonometric solutions of a real cubic with real roots. Descartes’ and Ferrari’s method for a bi-quadratic.