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Concept Maps

Theory of Equations — Concept Maps

Tamil Nadu Board · Class 12 · Mathematics

3 concept maps of Theory of Equations for Tamil Nadu Board Class 12 Mathematics, each also written out as a text outline.

45 questions25 flashcards8 formulas & key relations5 concepts

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3 Concept Maps

Theory of Equations – Complete Chapter Overview

Theory of Equations – Complete Chapter Overview

The map in words

  • Theory of Equations
    • Basics
      • Polynomial Definition
      • Degree and Leading Term
      • Monic Polynomial
      • Root vs Zero
      • Multiplicity of Root
    • Vieta Formulae
      • Quadratic
        • Sum of roots neg b over a
        • Product of roots c over a
      • Cubic
        • Sum neg b over a
        • Sum of pairs c over a
        • Product neg d over a
      • Quartic and Degree n
        • Alternating signs pattern
    • Fundamental Theorem
      • Every degree n poly has n roots in C
      • Odd degree has at least one real root
      • Even degree has even number real roots
    • Nature of Roots
      • Imaginary Roots
        • Complex Conjugate Theorem
        • Needs real coefficients
        • Occur in conjugate pairs
      • Irrational Roots
        • Surd Conjugate Theorem
        • Needs rational coefficients
        • Form p plus root q
      • Rational Roots
        • Discriminant is perfect square
    • Special Solving Methods
      • Even powers only
        • Substitute y for x squared
      • Sum of coefficients zero
        • x equals 1 is a root
      • Equal odd and even sums
        • x equals neg 1 is a root
      • Roots in AP
        • Assume a minus d, a, a plus d
      • Roots in GP
        • Assume alpha over r, alpha, alpha times r
      • Roots in HP
        • Reciprocals in AP
      • Imaginary or Surd root given
        • Use conjugate to get factor
      • Partly factored quartic
        • Rearrange then substitute
    • Reciprocal Equations
      • Type I
        • Coefficients same from both ends
        • Odd degree neg 1 is root
        • Even degree substitute y equals x plus 1 over x
      • Type II
        • Coefficients opposite from both ends
        • Odd degree 1 is root
        • Even degree 1 and neg 1 are roots
    • Descartes Rule
      • Sign changes in P of x
        • Upper bound positive roots
      • Sign changes in P of neg x
        • Upper bound negative roots
      • Lower bound imaginary roots
        • n minus m plus k
    • Rational Root Theorem
      • p divides constant term
      • q divides leading coefficient
      • List and test candidates

Flowchart showing how Vieta's formulas connect coefficients to sum and product of roots, enabling equation formation without explicit root calculation

Flowchart showing how Vieta's formulas connect coefficients to sum and product of roots, enabling equation formation without explicit root calculation

The map in words

  • Quadratic Equation ax² + bx + c = 0
    • Extract Coefficients a, b, c
      • Find Relationships
        • Sum: α + β = -b/a
          • Form New Equations x² - sum·x + product = 0
            • Solve Without Finding Roots
        • Product: αβ = c/a

Mind map showing the three Vieta's formulas for cubic equations and their relationships to coefficients

Mind map showing the three Vieta's formulas for cubic equations and their relationships to coefficients

The map in words

  • Vieta Formulas Cubic Equations
    • Three Roots: α, β, γ
      • Sum
        • α + β + γ = -b/a
        • First coefficient
      • Pair Products
        • αβ + βγ + γα = c/a
        • Second coefficient
      • All Product
        • αβγ = -d/a
        • Constant term
    • Applications
      • Form equations
      • New root relations
      • Solve progressions

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Frequently Asked Questions

What are the important topics in Theory of Equations for Tamil Nadu Board Class 12 Mathematics?
Key topics in Theory of Equations include Basics of Polynomial Equations, Vieta's Formulae – Relations Between Roots and Coefficients, Fundamental Theorem of Algebra, Nature of Roots – Complex Conjugate and Irrational (Surd) Roots. Study these first, then practise questions on each for the Tamil Nadu Board Class 12 board exam.
What do the concept maps for Theory of Equations show?
The 3 maps show how the ideas in Theory of Equations connect: Theory of Equations – Complete Chapter Overview; Flowchart showing how Vieta's formulas connect coefficients to sum and product of roots, enabling equation formation without explicit root calculation. Each map is also written out as an outline on this page.
How should I revise Theory of Equations for the Tamil Nadu Board Class 12 board exam?
Learn the core ideas first, then work through the 45 practice questions on Theory of Equations. Revise definitions regularly and use flashcards for quick recall before the exam.

Sources & Official References

Content is aligned to the official syllabus. Refer to the board website for the latest curriculum.

More resources for Theory of Equations

All Tamil Nadu Board Class 12 Mathematics Concept Maps

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