Page 1: Introduction
Quadratic equation: ax² + bx + c = 0 (a ≠ 0)
Roots: values of x satisfying equation.
Maximum two roots.
Chapter covers solving methods and nature of roots.
Page 2: Solution by Factorisation
Split middle term or factor directly.
Page 3: Completing the Square
Convert to (x + p)² = q
Steps: divide by a, move c, add (b/2a)² both sides.
Page 4: Quadratic Formula
Derived from completing square.
Universal method.
Page 5: Discriminant
- D > 0 → two distinct real roots
- D = 0 → equal real roots
- D < 0 → no real roots (complex)
Page 6: Nature of Roots Summary
| D | Roots |
|---|---|
| >0, perfect square | distinct rational |
| >0, not perfect | distinct irrational |
| =0 | equal rational |
| <0 | no real |
Page 7: Word Problems
Form quadratic from statement.
Common: numbers, area, speed, time, height.
Page 8: Key Formulas Summary
- Quadratic formula
- Discriminant D
- Sum of roots = -b/a
- Product = c/a
Page 9: Practice Questions - Easy (1-10)
- Standard form example.
- Discriminant of x² - 4x + 4.
- Solve x² - 5x + 6 = 0 factorisation.
- Nature of roots D=0.
- Quadratic formula for x² + 2x + 1 = 0.
- Sum of roots 2x² + 3x - 2 = 0.
- Product of roots x² - 4 = 0.
- Complete square x² + 6x + 5 = 0.
- D < 0 meaning.
- Roots equal when?
Page 10: Practice Questions - Medium (11-20)
- Solve 2x² - 7x + 3 = 0.
- Nature of roots 3x² - 4x + 2 = 0.
- Form equation with roots 2,3.
- Find k if roots equal in x² + kx + 9 = 0.
- Discriminant 4x² + 4x + 1 = 0.
- Word problem: number product 56, sum 15.
- Area problem: length = width + 5, area 84.
- Speed problem: time difference.
- Complete square for 2x² + 8x + 5 = 0.
- Find roots using formula 3x² - 5x - 2 = 0.
Page 11: Practice Questions - Hard (21-30)
- Find k for real and distinct roots.
- Advanced word problem: consecutive numbers.
- Time to reach ground projectile.
- Roots irrational proof.
- Form equation with given sum and product.
- Discriminant condition for rational roots.
- Speed of boat problem.
- Board level word problem.
- Equation with roots α, 1/α.
- Multiple step numerical.
Page 12: Discriminant Cases Table
All nature of roots.
Page 13: Common Mistakes
- Wrong sign in formula
- Forgetting ± in roots
- Wrong discriminant calculation
- Incorrect middle term split
- Wrong equation formation
Page 14: Previous Year Questions
Word problems, nature of roots, find k.
Page 15: Exam Tips
- Memorise quadratic formula
- Check discriminant first
- Show factorisation steps
- Verify roots by substitution
- Read word problems carefully
Page 16: Quick Revision Sheet
All methods, formulas, nature.
Page 17: Final Motivation
Chapter 4 complete! Quadratic equations is high-scoring.
Practice word problems.
Class 10 Maths unstoppable 🦖
Page 18: Extra Numericals
More solved problems.
Page 19: Word Problem Types
Numbers, area, speed, time.
Page 20: Quadratic Formula Derivation
Completing square method.
Page 21: Nature of Roots Cases
Detailed examples.
Page 22: Factorisation Tips
Middle term split method.
Page 23: Board Pattern Questions
Common types.
Page 24: Extra Practice
More questions.
Page 25: Sum and Product Relation
From Vieta’s formulas.
Page 26: Real-Life Applications
Projectile, profit, area.
Page 27: Thank You & Copyright
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