NCERT Solutions for Class 10 Mathematics Polynomials Chapter 2

NCERT solutions for Class 10 Mathematics Chapter Quadratic Equations – complete answers & explanations

Quadratic equations are an important part of Class 10 Mathematics that help students understand how algebraic expressions can be solved and applied in different situations. This chapter focuses on finding zeroes of polynomials, understanding their relationship with coefficients, and forming quadratic polynomials using given conditions. These concepts play a key role in building a strong foundation in algebra and are frequently asked in exams. With clear and reliable NCERT solutions, students can practise effectively and improve their problem-solving skills. Download the worksheet and practice alongside solutions for better clarity. With the right guidance and regular practice, students can gain confidence and accuracy in this chapter. Book a free trial now to get expert guidance.

What this NCERT chapter covers?

1. The chapter explains the concept of zeroes of polynomials and their graphical meaning. 
2. It helps students understand how to determine the number of zeroes from graphs. 
3. Students learn factorisation methods to find the zeroes of quadratic expressions. 
4. It focuses on verifying the relationship between zeroes and coefficients. 
5. The chapter builds strong algebraic manipulation and calculation skills. 
6. It teaches how to form quadratic polynomials when sum and product are given. 
7. Students learn to handle expressions involving fractions and negative values. 
8. It strengthens logical reasoning and step-by-step problem solving. 
9. The chapter improves accuracy in calculations and verification steps. 
10. It prepares students for exam-based questions on polynomials and equations. 
11. Students develop confidence in solving algebraic problems independently. 
12. Overall, it builds a solid base for advanced mathematics concepts. 

How to use these NCERT solutions?

1. Begin by reading each question carefully and understanding what is asked. 
2. Attempt all questions from the worksheet on your own first. 
3. Use the solutions only after completing your attempt. 
4. Compare your answers with the given ones step by step. 
5. Focus on the method used for factorisation and verification. 
6. Identify mistakes and revise those concepts again. 
7. Practice similar problems to strengthen understanding. 
8. Parents and teachers can guide students by explaining difficult steps. 
9. Follow the exact order of questions as given in the worksheet. 
10. Revise regularly to improve speed and accuracy in solving problems. 

Important tips & tricks for students

1. Always write the polynomial in standard form before solving. 
2. Be careful with signs while factorising expressions. 
3. Verify both sum and product of zeroes correctly. 
4. Practice solving problems involving fractions carefully. 
5. Show all steps clearly to avoid losing marks. 
6. Do not skip the verification step in answers. 
7. Learn common factorisation patterns for quicker solving. 
8. Keep calculations neat and organised. 
9. Read each question properly before attempting. 
10. Practice regularly to build confidence and accuracy. 

NCERT solutions – complete answer key

Exercise 2.1

1. Find the zeroes and verify the relationship

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

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

(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 

(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 

(iii) 6x² – 3 – 7x 
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 

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

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

(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:

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

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

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

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

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

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

Why NCERT solutions help students?

NCERT solutions help students understand the correct way to solve problems and present answers in exams. They improve clarity of concepts, strengthen problem-solving skills, and build confidence by providing accurate and structured answers aligned with exam expectations.

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