Theory of Equations — Class 12 Mathematics (Samacheer Kalvi)
TN State Board (Samacheer Kalvi) Class 12 Mathematics, Chapter 3. Polynomial roots, Vieta's formulas, nature of roots and transformations.
1. About this chapter
This chapter covers Theory of Equations as part of the Class 12 Samacheer Kalvi Mathematics curriculum. It deals with polynomial roots, vieta's formulas, nature of roots and transformations and builds conceptual understanding essential for the TN HSC Public Exam.
By the end of this chapter, students will be able to:
- Apply Vieta's formulas to find relationships between roots
- Transform and solve polynomial equations
2. Key concepts
- Concept 1: Apply Vieta's formulas to find relationships between roots.
- Concept 2: Transform and solve polynomial equations.
3. Important terms and formulas
| Term / Formula | Description |
|---|---|
| Apply Vieta's formulas to… | Apply Vieta's formulas to find relationships between roots |
| Transform and solve polynomial… | Transform and solve polynomial equations |
4. Worked examples
Example 1. Applying a key concept from this chapter.
Solution: Identify the relevant principle → apply the formula or rule → state the answer with correct units.
Example 2. A typical exam-style question on theory of equations.
Solution: Break the problem into steps, use the appropriate formula and verify the answer.
5. Common mistakes
- Mistake: Skipping units or forgetting to state them. Fix: Always write units alongside every quantity and answer.
- Mistake: Confusing similar terms or concepts in this chapter. Fix: Make a comparison table of the terms during revision.
6. Practice (exam-style)
- Define the main term or principle covered in Chapter 3.
- Give two real-life examples related to theory of equations.
- Solve a short numerical or descriptive question from this chapter.
- State one important formula and explain each symbol.
7. Answer key (hints)
- Refer to section 2 (Key concepts) above for the definition.
- Examples should be drawn from daily experience and local context.
- Apply the formula from section 3, show all steps clearly.
- Formula with units — refer to the textbook glossary for symbol meanings.
8. Quick revision
- Class 12 Mathematics — Chapter 3: Theory of Equations.
- Core idea: Polynomial roots, Vieta's formulas, nature of roots and transformations.
- Key outcomes: Apply Vieta's formulas to find relationships between roots; Transform and solve polynomial equations.
- Always revise diagrams / tables from the Samacheer Kalvi textbook before the exam.
