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Quadratic Equations and Theory of Equations — Study Plan

Telangana Open School (TOSS) · Class 12 · Mathematics

A step-by-step study plan for Quadratic Equations and Theory of Equations, Telangana Open School (TOSS) Class 12 Mathematics: what to learn first, what.

58 questions23 flashcards20 formulas & key relations5 concepts

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Study Plan

1
Day 1–2

Learn the Theory

Read the textbook chapter carefully. Note down definitions, formulas and key ideas. Focus on: Solving Quadratic Equations, Nature of Roots and Discriminant, Relations Between Roots and Coefficients.

2
Day 3

Practise

Solve the textbook exercises and extra practice questions. There are 58 questions available for this chapter.

3
Day 4

Revise & Test

Revise key points without looking at your notes. Take a practice quiz and mark weak areas for another pass.

4
Day 7

Spaced Revision

Come back to Quadratic Equations and Theory of Equations after a week. Use flashcards for quick recall and try past exam questions on this chapter.

What to Focus On

  • A root satisfies the equation when substituted for $ x $
  • Every quadratic equation has exactly two roots
  • If $ \alpha $ is a root, then $ (x - \alpha) $ is a factor of the quadratic expression
  • Factorization involves splitting the middle term and grouping
  • The zero-product property states that if $ ab = 0 $, then $ a = 0 $ or $ b = 0 $
  • This method works best when the roots are rational numbers
  • The quadratic formula is $ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $
  • The discriminant $ D = b^2 - 4ac $ determines the nature of the roots
  • If $ D > 0 $: two distinct real roots

Common Mistakes to Avoid

If the discriminant is negative, the quadratic has no solution.

The sum of roots is always \( \frac{b}{a} \), not \( -\frac{b}{a} \).

You can factorize any quadratic equation easily by splitting the middle term.

Memory Tips

Standard form of quadratic equation: ax² + bx + c = 0

Quadratic Formula: x = [-b ± √(b² - 4ac)] / (2a)

Discriminant D = b² - 4ac determines nature of roots

Sum of roots = -b/a, Product = c/a

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Frequently Asked Questions

What are the important topics in Quadratic Equations and Theory of Equations for Telangana Open School (TOSS) Class 12 Mathematics?
Key topics in Quadratic Equations and Theory of Equations include Solving Quadratic Equations, Nature of Roots and Discriminant, Relations Between Roots and Coefficients, Sign of Quadratic Expression and Extreme Values. Study these first, then practise questions on each for the Telangana Open School (TOSS) Class 12 board exam.
How should I revise Quadratic Equations and Theory of Equations for the Telangana Open School (TOSS) Class 12 board exam?
Learn the core ideas first, then work through the 58 practice questions on Quadratic Equations and 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 Quadratic Equations and Theory of Equations

All Telangana Open School (TOSS) Class 12 Mathematics Study Plan

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