NCERT Class 10 Mathematics Mathematics: Chapter 4 — MATHEMATICS
This chapter introduces quadratic equations, which are polynomial equations of degree two. It defines the standard form ax^2 + bx + c = 0, where a ≠ 0, and explains how these equations arise in real-life situations, such as calculating dimensions for a prayer hall or solving problems involving quantities and their products. The chapter traces the historical development of quadratic equations, mentioning contributions from Babylonian, Greek, Indian (Brahmagupta, Sridharacharya), and Arab mathematicians. It outlines the goal of studying various methods to find the roots (solutions) of quadratic equations and their applications. The initial section also begins to set up mathematical representations for word problems, demonstrating how to translate scenarios into quadratic equations.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 10 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 4 — MATHEMATICS |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 4 minutes |
| Word count | 723 |
Learning outcomes
- Define a quadratic equation and its standard form.
- Recognize quadratic equations in real-life contexts.
- Understand the historical development of quadratic equations.
- Formulate mathematical representations of problems leading to quadratic equations.
Vocabulary
| Word | Meaning |
|---|---|
| Quadratic polynomial | A polynomial of degree 2, in the form ax^2 + bx + c, where a ≠ 0. |
| Quadratic equation | An equation obtained by equating a quadratic polynomial to zero, ax^2 + bx + c = 0, where a ≠ 0. |
| Standard form | The form ax^2 + bx + c = 0, where terms are arranged in descending order of degree. |
| Roots | The solutions or values of the variable that satisfy a quadratic equation. |
| Carpet area | The usable floor area within a room or space. |
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Practice questions
- What is the standard form of a quadratic equation? Answer: The standard form is ax^2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0.
- Give an example of a quadratic equation. Answer: 2x^2 + x – 300 = 0 is an example of a quadratic equation.
- What condition must be met for ax^2 + bx + c = 0 to be a quadratic equation? Answer: The coefficient 'a' must not be equal to zero (a ≠ 0).
- Who is credited with giving an explicit formula to solve ax^2 + bx = c? Answer: Brahmagupta.
Frequently asked questions
What is a quadratic equation?
A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are real numbers and a ≠ 0.
What is the significance of the condition a ≠ 0 in a quadratic equation?
If a = 0, the equation becomes bx + c = 0, which is a linear equation, not a quadratic one.
Can you give an example of a real-life problem that can be represented by a quadratic equation?
Yes, finding the dimensions of a prayer hall with a given area and a relationship between its length and breadth can lead to a quadratic equation.
Who were some of the mathematicians who contributed to the study of quadratic equations?
Contributions were made by Babylonians, Euclid, Brahmagupta, Sridharacharya, Al-Khwarizmi, and Abraham bar Hiyya Ha-Nasi.
What will be studied in this chapter regarding quadratic equations?
This chapter will cover various ways of finding the roots of quadratic equations and their applications in daily life.
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Topics covered
NCERT Class 10 Mathematics — Mathematics — Chapter 4 — MATHEMATICS. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.