Theory of Equations
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Some Definitions
- real polynomial
- complex polynomial
- rational expression or function
- degree of a polynomial
- polynomial equation
- roots of an equation
- solution set
Remainder and Factor Theorems
- remainder theorem
- factor theorem
Identity Equations and Inequalities
- some standard identities
Graphical Interpretation
- zeros of an expression
- roots of the equation f of x equals g of x
Key Points in Solving an Equation
- domain of an equation
- extraneous roots
- loss of root
Graphs of Polynomial Functions
- leading coefficient test
- zeros of polynomial test
Equations Reducible to Quadratic
- methods and substitutions
Quadratic Equation and Nature of Roots
- quadratic equation with real coefficients
- quadratic equation with non-real coefficients
- finding range of a function involving a quadratic expression
- quadratic expression in two variables
Relation between Roots and Coefficients
- symmetric functions of roots
Common Roots
- condition for one common root
- condition for both common roots
Higher Degree Equations
- relation between roots and coefficients
- solving cubic equations
- repeated roots
Quadratic Function
- analysis and graphs
Location of Roots
- Rolle's theorem to locate the roots
- solving inequalities using location of roots
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