NCERT Solutions for Class 10 Mathematics Chapter 2 Polynomials

This worksheet provides NCERT Solutions for Class 10 Mathematics Chapter Polynomials. This worksheet helps students understand how to identify the number of zeroes of a polynomial from graphs, find the zeroes of polynomial expressions, verify the relationship between the sum and product of zeroes, and form quadratic polynomials using given values. This chapter is important because it strengthens algebraic thinking and helps students understand how polynomial equations behave. The worksheet includes complete and accurate NCERT Solutions presented exactly as given, helping students practise and revise effectively.

Chapter summary: 

This NCERT chapter is purely concept-based and focuses on mathematical problem solving. Students work with polynomial expressions, analyse graphs to determine the number of zeroes, and verify algebraic relationships between coefficients and roots. The chapter mainly focuses on developing understanding through calculation and structured exercises that help students observe patterns in polynomials and quadratic expressions.

What this NCERT chapter covers?

• Understanding zeroes of polynomials 
• Identifying the number of zeroes from graphs 
• Verifying the relationship between zeroes and coefficients 
• Factoring polynomial expressions 
• Forming quadratic polynomials using given sum and product values 
• Strengthening algebraic calculation and reasoning 

How to use these NCERT solutions?

Students should first read each question in this worksheet carefully and try solving it on their own before checking the answer. After attempting the problems, they can compare their solutions with the provided NCERT Solutions to understand the correct method used. Parents and teachers can guide students while verifying steps and calculations. The answers follow the exact order of the worksheet, which makes revision easier and helps students understand the NCERT method of solving polynomial problems.

Student tips & learning tricks

Students should write polynomial expressions neatly before solving them. While factoring, they should carefully check the signs and coefficients. A common mistake is calculating the sum or product of zeroes incorrectly, so verifying each step is important. Practising similar polynomial questions can improve accuracy and confidence in solving algebra problems.

Why NCERT solutions are important?

NCERT Solutions help students follow the correct mathematical methods recommended in the NCERT curriculum. They support strong conceptual understanding and help students prepare for school tests and board examinations. Learning through NCERT-aligned solutions also improves problem-solving skills and builds confidence in mathematics.

Complete answer key – NCERT solutions

Exercise 2.1

Number of zeroes of p(x) in each graph:

1. (i) 2 
2. (ii) 1 
3. (iii) 3 
4. (iv) 0 
5. (v) 4 
6. (vi) 3 

Find the zeroes and verify the relationship

1. (i) x² – 2x – 8 
x² – 2x – 8 = (x – 4)(x + 2) 
Zeroes: 4, –2 
Sum = 4 + (–2) = 2 = –(–2)/1 
Product = 4 × (–2) = –8 = (–8)/1 

2. (ii) 4s² – 4s + 1 
4s² – 4s + 1 = (2s – 1)(2s – 1) 
Zeroes: 1/2, 1/2 
Sum = 1/2 + 1/2 = 1 = –(–4)/4 
Product = (1/2)(1/2) = 1/4 = 1/4 

3. (iii) 6x² – 7x – 3 
6x² – 7x – 3 = (3x + 1)(2x – 3) 
Zeroes: 3/2, –1/3 
Sum = 3/2 + (–1/3) = 7/6 = –(–7)/6 
Product = (3/2)(–1/3) = –1/2 = (–3)/6 

4. (iv) 4u² + 8u 
4u² + 8u = 4u(u + 2) 
Zeroes: 0, –2 
Sum = 0 + (–2) = –2 = –8/4 
Product = 0 × (–2) = 0 = 0/4 

5. (v) t² – 15 
t² – 15 = (t – √15)(t + √15) 
Zeroes: √15, –√15 
Sum = √15 + (–√15) = 0 = 0/1 
Product = (√15)(–√15) = –15 = –15/1 

6. (vi) 3x² – x – 4 
3x² – x – 4 = (3x – 4)(x + 1) 
Zeroes: 4/3, –1 
Sum = 4/3 + (–1) = 1/3 = –(–1)/3 
Product = (4/3)(–1) = –4/3 = (–4)/3 

Exercise 4.2

Find quadratic polynomial:

1. (i) Sum = –1, Product = 1/4 
Polynomial: x² – (–1)x + 1/4 = x² + x + 1/4 

2. (ii) Sum = 1/2, Product = 3 
Polynomial: x² – (1/2)x + 3 

3. (iii) Sum = 0, Product = 5 
Polynomial: x² – 5 

4. (iv) Sum = 1, Product = 1 
Polynomial: x² – x + 1 

5. (v) Sum = –1/4, Product = 1/4 
Polynomial: x² + (1/4)x + 1/4 

6. (vi) Sum = 4, Product = 1 
Polynomial: x² – 4x + 1 
 

Build confidence in algebra with these accurate NCERT Solutions for Class 10 Mathematics Chapter Polynomials and support your learning with structured practice and clear explanations. 
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