NCERT Solutions Class 10 Maths Chapter 4 teaches you three powerful methods to solve quadratic equations: factorization, completing the square, and the quadratic formula. You’ll learn when to use each method, how to find roots using the discriminant to determine if solutions are real or imaginary, and solve real-world problems involving areas, speeds, and ages. Master the nature of roots and apply these techniques to crack both board exams and competitive tests.
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All exercises with step-by-step solutions | Updated 2025-26 | Free Download
Download PDF (Free)NCERT Solutions Class 10 Maths Chapter 4 Quadratic Equations – Complete Guide
NCERT Class 10 Chapter 4 – Quadratic Equations introduces you to one of the most important algebraic concepts in CBSE mathematics. You’ll discover what makes an equation quadratic (equations of the form ax² + bx + c = 0, where a ≠ 0) and why these equations appear frequently in physics, engineering, and everyday problem-solving scenarios like calculating areas, projectile motion, and profit-loss situations.
📊 CBSE Class 10 Maths Chapter 4 – Exam Weightage & Marking Scheme
| CBSE Board Marks | 5 Marks |
| Unit Name | Algebra |
| Difficulty Level | Medium |
| Importance | Medium |
| Exam Types | CBSE Board, State Boards |
| Typical Questions | 1-2 questions |
This chapter carries 5 marks in your CBSE board exam, making it a medium-weightage topic that requires thorough practice. You’ll learn four powerful methods to solve quadratic equations: factorization (splitting the middle term), completing the square method, using the quadratic formula (the most versatile approach), and graphical representation. The discriminant (b² – 4ac) becomes your tool to determine whether roots are real, equal, or imaginary without actually solving the equation.
Expect a mix of question types in your board exam: 2-mark questions testing basic factorization and formula application, 3-mark problems involving word problems (like age problems, speed-distance scenarios, or geometric applications), and occasionally 4-mark questions combining multiple concepts. The chapter builds directly on your knowledge of polynomials from Chapter 2, so understanding factor theorem and zeros of polynomials will help you excel here.
Quick Facts – Class 10 Chapter 4
| 📖 Chapter Number | Chapter 4 |
| 📚 Chapter Name | Quadratic Equations |
| ✏️ Total Exercises | 3 Exercises |
| ❓ Total Questions | 13 Questions |
| 📅 Updated For | CBSE Session 2025-26 |
Mastering quadratic equations opens doors to advanced mathematics in Class 11 and 12, particularly in calculus and coordinate geometry. With consistent practice of NCERT exercises and previous year CBSE questions, you’ll develop the confidence to tackle any quadratic equation problem efficiently. Focus on understanding when to use which method – this strategic thinking is what examiners reward with full marks.
NCERT Solutions Class 10 Maths Chapter 4 – All Exercises PDF Download
Download exercise-wise NCERT Solutions PDFs for offline study
| Exercise No. | Topics Covered | Download PDF |
|---|---|---|
| Exercise 4.1 | Complete step-by-step solutions for 2 questions | 📥 Download PDF |
| Exercise 4.2 | Complete step-by-step solutions for 6 questions | 📥 Download PDF |
| Exercise 4.3 | Complete step-by-step solutions for 5 questions | 📥 Download PDF |
Quadratic Equations – Key Formulas & Concepts
Quick reference for CBSE exams
| Formula | Description | When to Use |
|---|---|---|
| Standard Form of Quadratic Equation \(ax^2 + bx + c = 0\) | The general form of a quadratic equation where a, b, and c are constants and a ≠ 0. Note: Make sure the equation is in this form before applying any formulas. a, b, and c are coefficients including their signs. | Identifying coefficients a, b, and c for use in other formulas (e.g., quadratic formula, discriminant). |
| Quadratic Formula \(x = \frac{-b \pm \sqrt{b^2 – 4ac}}{2a}\) | Finds the roots (solutions) of the quadratic equation ax² + bx + c = 0. Note: Remember to consider both the ‘+’ and ‘-‘ cases to find both roots. Careful with signs! | When you need to find the exact roots of any quadratic equation, especially when factoring is difficult or impossible. |
| Discriminant \(D = b^2 – 4ac\) | Determines the nature of the roots of the quadratic equation ax² + bx + c = 0. Note: If D > 0: two distinct real roots. If D = 0: two equal real roots. If D < 0: no real roots (imaginary roots). | Before solving a quadratic equation, to determine if the roots are real and distinct, real and equal, or not real. |
| Sum of Roots \(\alpha + \beta = -\frac{b}{a}\) | Calculates the sum of the roots (α and β) of the quadratic equation ax² + bx + c = 0. Note: Remember the negative sign! It’s -b/a, not b/a. | When you need to find the sum of the roots without actually calculating the roots themselves. Useful for relationship problems. |
| Product of Roots \(\alpha \cdot \beta = \frac{c}{a}\) | Calculates the product of the roots (α and β) of the quadratic equation ax² + bx + c = 0. Note: This is simply c/a. No negative sign here. | When you need to find the product of the roots without actually calculating the roots themselves. Useful for relationship problems. |
| Forming a Quadratic Equation from Roots \(x^2 – (\alpha + \beta)x + \alpha\beta = 0\) | Creates a quadratic equation given its roots (α and β). Note: Make sure to substitute the values of the sum and product of the roots correctly. | When you are given the roots of a quadratic equation and need to find the equation itself. |
| Perfect Square Trinomial \(a^2 + 2ab + b^2 = (a+b)^2\) or \(a^2 – 2ab + b^2 = (a-b)^2\) | Recognizing and factoring perfect square trinomials. Note: Carefully check the sign of the middle term (2ab) to determine whether it’s (a+b)² or (a-b)². | While solving quadratic equations by completing the square or factoring. |
| Completing the Square (General) \(x^2 + bx + (\frac{b}{2})^2 = (x + \frac{b}{2})^2\) | Manipulating a quadratic expression to create a perfect square trinomial. Note: Remember to add the same value (\((\frac{b}{2})^2\)) to both sides of the equation to maintain equality. b is the coefficient of the ‘x’ term. | When you need to solve a quadratic equation by completing the square method or transforming the equation into vertex form. |
| Nature of Roots based on Discriminant If \(D > 0\): Two distinct real roots. If \(D = 0\): Two equal real roots. If \(D < 0\): No real roots. | Summary of root types based on the discriminant’s value. Note: Important for understanding the solutions without fully solving. | After calculating the discriminant, to quickly determine the type of roots the quadratic equation has. |
| Relationship between Roots and Coefficients If roots are α and β, then the quadratic equation is a(x – α)(x – β) = 0 | Expressing the quadratic equation using its roots and a constant factor a. Note: This is a more general form than using the sum and product of roots, as it allows for scaling the entire equation. | Constructing a quadratic equation when the roots are known, and you want to include a leading coefficient ‘a’. |
Frequently Asked Questions – NCERT Class 10 Maths Chapter 4
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| NCERT Class 10 Maths All Chapters | View Solutions |
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| NCERT Class 10 English Solutions | View Solutions |