Mathematics becomes more fascinating when we move into concepts like Complex Numbers (सम्मिश्र संख्याएँ) and Quadratic Equations (द्विघातीय समीकरण). Chapter 4 of the NCERT Class 10 Mathematics (Hindi Medium) introduces students to these two important ideas in a clear and structured way. This chapter helps students understand how to handle negative square roots and how to find solutions of equations that go beyond real numbers. You can download the NCERT Class 10 Maths Hindi Chapter 4 PDF here to study the complete chapter with solved examples and exercises.
I am writing about this topic because many students find complex numbers and quadratic equations a bit intimidating at first. But once they understand the logic behind them, it becomes one of the most interesting parts of algebra. These topics are not just important for board exams but also for higher classes, especially in science and engineering streams. Understanding this chapter builds strong problem-solving ability and helps students think beyond traditional number systems. Let’s explore what makes this chapter so important and how you can easily master it.
About NCERT Class 10 Maths Chapter 4 – सम्मिश्र संख्याएँ और द्विघातीय समीकरण
This chapter combines two fundamental algebraic concepts — complex numbers and quadratic equations. It starts with explaining how negative numbers under a square root are represented using the symbol ‘i’ (called iota) and then progresses to finding roots of quadratic equations.
Key Concepts Covered in the Chapter
- Complex Numbers (सम्मिश्र संख्याएँ)
- Introduction to imaginary numbers where i = √–1
- Representation of a complex number as a + bi
- Real part (a) and Imaginary part (b)
- Basic operations on complex numbers – addition, subtraction, multiplication, and division
- Quadratic Equations (द्विघातीय समीकरण)
- Standard form: ax² + bx + c = 0
- Methods of solving quadratic equations:
- Factorisation method
- Completing the square method
- Quadratic formula: x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}x=2a−b±b2−4ac
- Nature of roots based on discriminant (D = b² – 4ac)
Understanding the Discriminant
| Discriminant (D) | Nature of Roots |
|---|---|
| D > 0 | Two distinct real roots |
| D = 0 | Two equal real roots |
| D < 0 | Complex (imaginary) roots |
This table is important for understanding whether the equation gives real or complex solutions.
Real-Life Connection of Quadratic Equations
Quadratic equations are not just theoretical. They are used in areas like physics (projectile motion), economics (profit and loss curves), and even construction and engineering. For example, when calculating the maximum height of a ball thrown upwards, we use a quadratic equation to find the value of time and height.
Complex numbers also play a role in electrical circuits, quantum mechanics, and computer simulations. Though they seem abstract in school, they are extremely practical in higher studies and modern applications.
NCERT Class 10 Maths Chapter 4 PDF Download
Students can download the NCERT Class 10 Maths Hindi Chapter 4 – सम्मिश्र संख्याएँ और द्विघातीय समीकरण PDF directly from here.
