Class 10 Maths Chapter 2 Exercise 2.1 Solutions – Polynomials | Assam Eduverse

Welcome to Assam Eduverse, your trusted resource for Class 10 study materials. Below are the detailed NCERT solutions for Chapter 2: Polynomials – Exercise 2.1, fully aligned with the latest SEBA and NCERT curriculum (2025–26).

📘 Chapter 2: Polynomials

🧮 Exercise 2.1 – NCERT Solutions

✅ Question 1:

Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.

(i) x² – 2x – 8

Solution:
Factorizing:
x² – 2x – 8 = (x – 4)(x + 2)
Zeroes: x = 4, –2

Verification:
Sum = 4 + (–2) = 2 = –(–2)/1
Product = 4 × (–2) = –8 = –8/1
✅ Relationship verified

(ii) x² + 4x + 3

Factor: (x + 1)(x + 3)
Zeroes: x = –1, –3

Verification:
Sum = –1 + (–3) = –4 = –4/1
Product = (–1)(–3) = 3 = 3/1
✅ Verified

(iii) x² + x – 6

Factor: (x + 3)(x – 2)
Zeroes: x = –3, 2

Sum = –3 + 2 = –1 = –1/1
Product = –3 × 2 = –6 = –6/1
✅ Verified

(iv) x² + 2x + 1

Factor: (x + 1)(x + 1)
Zeroes: x = –1, –1

Sum = –1 + (–1) = –2 = –2/1
Product = (–1)(–1) = 1 = 1/1
✅ Verified

(v) x² – 3

This is a difference of squares:
x² – 3 = (x – √3)(x + √3)
Zeroes: √3 and –√3

Sum = √3 + (–√3) = 0 = –0/1
Product = √3 × (–√3) = –3 = –3/1
✅ Verified

(vi) 2x² + 5x – 3

Factor: (2x – 1)(x + 3)
Zeroes: x = 1/2, –3

Sum = 1/2 + (–3) = –5/2 = –5/2
= –b/a = –5/2
Product = (1/2)(–3) = –3/2 = c/a = –3/2
✅ Verified