Summary

SUMMARY

In this chapter we studied

·               Vieta’s Formula for polynomial equations of degree 2,3, and n>3.

·               The Fundamental Theorem of Algebra : A polynomial of degree n  ≥ 1 has at least one root in C.

·               Complex Conjugate Root Theorem : Imaginary (nonreal complex) roots occur as conjugate

pairs, if the coefficients of the polynomial are real.

·               Rational Root Theorem : Let a_n xⁿ+…+a₁ x+ a0 with a_n ≠  0 and a₀≠ 0 , be a polynomial with integer coefficients. If p/q , with ( p, q) = 1, is a root of the polynomial, then p is a factor of a₀ and q is a factor of a_n.

·               Methods to solve some special types of polynomial equations like polynomials having only even powers, partly factored polynomials, polynomials with sum of the coefficients is zero, reciprocal equations.

·               Descartes Rule : If p is the number of positive roots of a polynomial P(x) and s is the number of sign changes in coefficients of P(x) , then s - p is a nonnegative even integer.