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Theory of Equations

Tamil Nadu Board · Class 12 · Mathematics

Complete topic list for Theory of Equations in Tamil Nadu Board Class 12 Mathematics. Key concepts, sub-topics, and what to focus on for board exams.

45 questions25 flashcards5 concepts

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4 Topics · Tamil Nadu Board Class 12 Mathematics

Topics in Theory of Equations

1

1. Basics of Polynomial Equations

  • A polynomial of degree n is P(x) = aₙxⁿ + aₙ₋₁xⁿ⁻¹ + ... + a₁x + a₀, where aₙ ≠ 0.
  • The equation P(x) = 0 is called a polynomial equation.
  • A value c ∈ ℂ satisfying P(c) = 0 is called a root or zero of the polynomial.
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2. Vieta's Formulae – Relations Between Roots and Coefficients

  • Vieta's formulae connect the COEFFICIENTS of a polynomial to SUMS and PRODUCTS of its roots.
  • For a quadratic ax² + bx + c = 0 with roots α, β: α + β = -b/a and αβ = c/a.
  • A quadratic with roots α and β is: x² - (α + β)x + αβ = 0.
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3. Fundamental Theorem of Algebra

  • FUNDAMENTAL THEOREM: Every polynomial equation of degree n ≥ 1 has at least one root in ℂ (complex numbers).
  • Consequence: A polynomial equation of degree n has EXACTLY n roots in ℂ when counted with multiplicity.
  • A polynomial equation of degree n cannot have MORE than n roots, even counting multiplicity.
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4. Nature of Roots – Complex Conjugate and Irrational (Surd) Roots

  • COMPLEX CONJUGATE ROOT THEOREM: If a + ib (b ≠ 0) is a root of a polynomial with REAL coefficients, then a - ib is also a root.
  • Non-real complex (imaginary) roots always occur in CONJUGATE PAIRS for polynomials with real coefficients.
  • Since imaginary roots come in pairs, an odd-degree polynomial with real coefficients always has at least one real root.

Key Concepts

A polynomial equation of degree nVieta's formulae establish algebraic relationships betweenWhen roots of a polynomialEvery polynomial equation of degree nIf a polynomial equation has real

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 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, Mind map showing the three Vieta's formulas for cubic equations and their relationships to coefficients. These are the concepts Tamil Nadu Board Class 12 examiners draw on most — study them first, then practise related questions.
How to score full marks in Theory of Equations — Tamil Nadu Board Class 12 Mathematics?
Understand the core concepts first, then work through the 45 practice questions available for this chapter. Revise formulas and 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.

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All 12 chapters — Tamil Nadu Board Class 12 Mathematics Syllabus

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