Theory of Equations

IIT-JEE · Class 11 · Mathematics

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What’s covered

  • topics
    • 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