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Theory of Equations — Syllabus

Tamil Nadu Board · Class 12 · Mathematics

What Theory of Equations covers in Tamil Nadu Board Class 12 Mathematics: 4 topics, for the 2026-27 session. Topics include Basics of Polynomial.

45 questions25 flashcards8 formulas & key relations5 concepts

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4 Topics · Tamil Nadu Board Class 12 Mathematics · 2026-27

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.
2

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.
3

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.
4

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

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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.
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.

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All Tamil Nadu Board Class 12 Mathematics Syllabus

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