Algebra traditionally deals with equations and systems of equations. The simplest types of equations in Algebra, are the so called polynomial equations.
The aim of this short book is to help the students to master some fundamental techniques in solving polynomial equations using appropriate definitions, concepts and theorems.
This book consists of three chapters.
The first chapter deals with first and second order equations, (Quadratic equations).
The second chapter deals with equations reducible to quadratic equations, (Bi quadratic equations), or equations solved by means of an appropriate substitution. The method of substitution, in solving equations, is extremely powerful; however there are no general rules as to which substitution is the proper one for each problem. Substitution is a highly individual method of solution.
In the third chapter we state some general properties of polynomial equations, (The fundamental theorem of Algebra, proved rigorously for the first time by the great C. F. Gauss in 1799, the Remainder Theorem, the Factor Theorem, and the complex conjugate roots Theorem, the Rational Roots Theorem, etc.).
All solved examples and problems to be solved are carefully selected, in order to help students to gradually acquire the necessary techniques, experience and computational skills in problem solving.
All problems are supplied with answers.