NCERT Solutions Class 10 Maths Chapter 2 provides complete, step-by-step solutions to all Polynomials questions, helping you understand how to find zeros of quadratic polynomials, verify relationships between zeros and coefficients, and form polynomial equations from given zeros. You’ll learn graphical methods to visualize polynomial behavior, division algorithms for finding remainders, and practical techniques to solve real-world problems involving quadratic expressions that frequently appear in CBSE board exams.
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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 2 Polynomials – Complete Guide
NCERT Class 10 Chapter 2 Polynomials builds upon your foundation from Class 9, taking you deeper into algebraic expressions that form the backbone of higher mathematics. You’ll explore polynomials in one variable, learn to classify them by degree (linear, quadratic, cubic), and understand how to perform operations like addition, subtraction, and multiplication with ease.
📊 CBSE Class 10 Maths Chapter 2 – 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 |
The heart of this chapter lies in understanding the geometrical meaning of zeros of polynomials and their relationship with coefficients. You’ll discover the division algorithm for polynomials, which works remarkably similar to dividing numbers, and learn how to find remainders without complete division. The relationship between zeros and coefficients of quadratic polynomials is particularly crucial for CBSE board exams, as it frequently appears in 2-3 mark questions.
This chapter carries approximately 5 marks in your CBSE Class 10 board examination, typically appearing as a mix of MCQs (1 mark), short answer questions (2 marks), and occasionally long answer problems (3 marks). You’ll encounter questions asking you to find zeros graphically, verify relationships between zeros and coefficients, or apply the division algorithm to solve polynomial equations.
Quick Facts – Class 10 Chapter 2
| 📖 Chapter Number | Chapter 2 |
| 📚 Chapter Name | Polynomials |
| ✏️ Total Exercises | 2 Exercises |
| ❓ Total Questions | 3 Questions |
| 📅 Updated For | CBSE Session 2025-26 |
Mastering polynomials is essential not just for your board exams, but also for understanding quadratic equations, coordinate geometry, and calculus in higher classes. The concepts you learn here have real-world applications in physics, economics, and engineering, where polynomial functions model everything from projectile motion to profit calculations. With consistent practice of NCERT solutions and sample problems, you’ll build strong algebraic skills that will serve you throughout your academic journey.
NCERT Solutions Class 10 Maths Chapter 2 – All Exercises PDF Download
Download exercise-wise NCERT Solutions PDFs for offline study
| Exercise No. | Topics Covered | Download PDF |
|---|---|---|
| EXERCISE 2.1 | Complete step-by-step solutions for 1 questions | 📥 Download PDF |
| EXERCISE 2.2 | Complete step-by-step solutions for 2 questions | 📥 Download PDF |
Polynomials – Key Formulas & Concepts
Quick reference for CBSE exams
| Formula | Description | When to Use |
|---|---|---|
| General form of a Polynomial \(p(x) = a_n x^n + a_{n-1} x^{n-1} + … + a_1 x + a_0\) | Represents a polynomial of degree ‘n’, where a_n, a_{n-1}, …, a_0 are constants and a_n ≠ 0 Note: The highest power of x with a non-zero coefficient determines the degree. | Understanding the structure of polynomials, identifying coefficients and degree. |
| Zeroes of a Polynomial \(p(k) = 0\) | Defines a zero (or root) ‘k’ of a polynomial p(x) as the value of x for which p(x) equals zero. Note: Geometrically, zeroes are the x-intercepts of the polynomial’s graph. | Finding the values of x that make the polynomial equal to zero, solving polynomial equations. |
| Relationship between zeroes and coefficients (Quadratic Polynomial) \(\alpha + \beta = -\frac{b}{a}\) | Relates the sum of zeroes (\(\alpha\) and \(\beta\)) of a quadratic polynomial \(ax^2 + bx + c\) to its coefficients. Note: Remember the negative sign! It’s the negative of the coefficient of x divided by the coefficient of x². | Finding the sum of zeroes without actually calculating the zeroes, verifying the roots, solving problems involving relationships between roots. |
| Product of zeroes (Quadratic Polynomial) \(\alpha \beta = \frac{c}{a}\) | Relates the product of zeroes (\(\alpha\) and \(\beta\)) of a quadratic polynomial \(ax^2 + bx + c\) to its coefficients. Note: It’s the constant term divided by the coefficient of x². | Finding the product of zeroes without calculating the zeroes, verifying roots, solving problems relating roots. |
| Forming a Quadratic Polynomial given zeroes \(p(x) = k[x^2 – (\alpha + \beta)x + \alpha \beta]\) | Constructs a quadratic polynomial when the sum and product of its zeroes are known. ‘k’ is any non-zero constant. Note: Don’t forget the constant ‘k’. It means there are infinitely many polynomials with the same zeroes. | Creating a polynomial equation when the zeroes are given or their sum and product are provided. |
| Division Algorithm for Polynomials \(p(x) = g(x) \cdot q(x) + r(x)\) | States that for any two polynomials p(x) and g(x) (where g(x) ≠ 0), there exist polynomials q(x) and r(x) such that p(x) = g(x) * q(x) + r(x), where degree of r(x) < degree of g(x). Note: p(x) is the dividend, g(x) is the divisor, q(x) is the quotient, and r(x) is the remainder. Always check that the degree of r(x) is less than the degree of g(x). | Dividing one polynomial by another, finding the quotient and remainder, verifying polynomial division. |
| Relationship between zeroes and coefficients (Cubic Polynomial) \(\alpha + \beta + \gamma = -\frac{b}{a}\) | Relates the sum of zeroes (\(\alpha\), \(\beta\), and \(\gamma\)) of a cubic polynomial \(ax^3 + bx^2 + cx + d\) to its coefficients. Note: Similar to the quadratic case, it’s the negative of the coefficient of x² divided by the coefficient of x³. | Finding the sum of the zeroes of a cubic polynomial without finding the individual zeroes. |
| Sum of product of zeroes taken two at a time (Cubic Polynomial) \(\alpha\beta + \beta\gamma + \gamma\alpha = \frac{c}{a}\) | Relates the sum of the product of zeroes taken two at a time (\(\alpha\), \(\beta\), and \(\gamma\)) of a cubic polynomial \(ax^3 + bx^2 + cx + d\) to its coefficients. Note: It’s the coefficient of x divided by the coefficient of x³. | Solving problems relating to the sum of the product of roots taken two at a time. |
| Product of zeroes (Cubic Polynomial) \(\alpha \beta \gamma = -\frac{d}{a}\) | Relates the product of zeroes (\(\alpha\), \(\beta\), and \(\gamma\)) of a cubic polynomial \(ax^3 + bx^2 + cx + d\) to its coefficients. Note: It’s the negative of the constant term divided by the coefficient of x³. | Finding the product of the zeroes of a cubic polynomial without finding the individual zeroes. |
Frequently Asked Questions – NCERT Class 10 Maths Chapter 2
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| NCERT Class 10 Maths All Chapters | View Solutions |
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| NCERT Class 10 English Solutions | View Solutions |