NCERT Solutions for Class 10 Mathematics Chapter 2 Polynomials

This worksheet for Class 10 Mathematics Chapter 2 Polynomials helps students understand important concepts related to polynomials, including zeroes and their relationships. This worksheet provides complete and accurate NCERT Solutions that strictly follow the NCERT pattern. The chapter is important because it builds a strong base in algebra and helps students understand how to factorise expressions, find zeroes, and verify relationships between them. 

Chapter summary:

This worksheet focuses on mathematical problem-solving activities such as identifying the number of zeroes from graphs and solving algebraic expressions. The main learning focus is understanding polynomials and verifying relationships between zeroes and coefficients. The worksheet is activity-based in terms of calculations and verification.

What this NCERT chapter covers?

• Understanding polynomials and their zeroes  
• Finding the number of zeroes from graphs  
• Factorisation of algebraic expressions  
• Verifying the relationship between zeroes and coefficients  
• Forming quadratic polynomials from given sum and product  

How to use these NCERT solutions?

Students should first attempt all questions in the worksheet on their own before checking the answers. Parents and teachers can use these solutions to guide students and explain each step clearly. The solutions follow the exact NCERT order and structure, making them useful for revision and better understanding of concepts.

Student tips & learning tricks

• Carefully factorise each polynomial step by step  
• Always check the signs while calculating sum and product  
• Practice reading graphs properly to identify zeroes  
• Revise formulas related to sum and product of zeroes  
• Avoid calculation mistakes by verifying each step  

Why NCERT solutions are important?

NCERT Solutions are important because they follow the official CBSE curriculum and ensure correct understanding of concepts. They help students build a strong foundation in mathematics, improve accuracy, and prepare effectively for exams. These solutions also boost confidence by providing reliable and structured answers.

Complete answer key – NCERT solutions

Exercise 2.1

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  

2. 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  

Master Class 10 Mathematics Polynomials with accurate NCERT Solutions and improve problem-solving skills with step-by-step practice.  
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