Quadratic
Equations
Complete chapter resources for CBSE Class 10 Mathematics — topic breakdown, key formulas, sample questions, previous year board questions, and instant AI question paper generation.
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- Standard form: ax² + bx + c = 0, a ≠ 0
- Quadratic formula: x = (−b ± √(b²−4ac)) / 2a
- Discriminant: D = b² − 4ac
- Sum of roots: α + β = −b / a
- Product of roots: αβ = c / a
- Equal roots condition: D = 0 ⟹ b² = 4ac
What this chapter covers
A quadratic equation in one variable is a polynomial equation of degree 2, written in the standard form ax² + bx + c = 0, where a, b, c are real numbers and a ≠ 0. The solutions — values of x that satisfy the equation — are called roots or zeroes of the quadratic. NCERT Chapter 4 begins by defining this standard form, distinguishing quadratic equations from linear and higher-degree polynomials, and practising the skill of representing real-world situations as quadratic equations before attempting to solve them.
The chapter teaches four approaches to finding roots: recognising roots by inspection, factorising by splitting the middle term (product-sum method), transforming the equation by completing the square, and applying the quadratic formula — also known as Sridharacharya's formula — x = (−b ± √D) / 2a. A central unifying concept is the discriminant D = b² − 4ac, which determines the nature of roots: two distinct real roots when D > 0, two equal real roots when D = 0, and no real roots when D < 0.
Board questions consistently include word problems where a real-world scenario — involving speed and distance, areas of rectangles, time-and-work rates, or age relationships — must first be modelled as a quadratic equation, solved, and then interpreted in context. These application problems typically carry the highest marks in the chapter and demand both algebraic accuracy and careful reading of the problem setup.
What's inside Chapter 4
As per NCERT Class 10 Mathematics (CBSE syllabus)
How this chapter fits in
Useful for setting question difficulty and cross-chapter papers.
Equations
Marks & question-type breakdown
Typical pattern based on CBSE Class 10 board papers from the last five years.
| Question type | Marks | Typical count | What's usually tested |
|---|---|---|---|
| MCQ / Objective | 1 | 1–2 | Discriminant value, nature of roots, or identifying whether an equation is quadratic |
| Very Short Answer | 2 | 1 | Find roots by factorisation, check nature of roots, or find k for equal roots |
| Short Answer | 3 | 1 | Completing the square or a straightforward word problem modelled as a quadratic |
| Long Answer / Word Problem | 4–5 | 1 | Real-life application — speed-distance, area, work-rate, or age problems |
| Total (approximate) | 6–8 | 4–5 | Weightage varies across paper sets and years |
8 sample questions — generated by MarksZen AI
Aligned to CBSE Class 10 Mathematics Chapter 4. Covers all question types across Easy, Medium, and Hard difficulty.
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From CBSE board examinations
Actual questions from past Class 10 Mathematics board papers — Quadratic Equations chapter.
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question paper in 2 minutes.
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- All 4 topics of this chapter
- MCQ + short answer + word problems
- Answer key included
- PDF export ready