NCERT Class 10 Maths – Chapter 2: Polynomials
Exercise 2.2 – Find Zeroes and Verify Relationship
Class: 10
Subject: Mathematics
Chapter: Polynomials
Exercise: 2.2
Important Formula Used
For a quadratic polynomial: ax² + bx + c
- Sum of zeroes = -b/a
- Product of zeroes = c/a
Question 1: Find the zeroes and verify relationship
(i) x² − 2x − 8
x² − 2x − 8 = (x − 4)(x + 2)
Zeroes: 4, −2
Sum = 4 + (−2) = 2 = −(−2)/1 ✔
Product = 4 × (−2) = −8 = c/a ✔
(ii) 4s² − 4s + 1
= (2s − 1)²
Zeroes: 1/2, 1/2
Sum = 1/2 + 1/2 = 1 = −(−4)/4 ✔
Product = 1/4 = 1/4 ✔
(iii) 6x² − 7x − 3
= (3x + 1)(2x − 3)
Zeroes: −1/3, 3/2
Sum = −1/3 + 3/2 = 7/6 = −(−7)/6 ✔
Product = (−1/3)(3/2) = −1/2 = −3/6 ✔
(iv) 4u² + 8u
= 4u(u + 2)
Zeroes: 0, −2
Sum = −2 = −8/4 ✔
Product = 0 = 0/4 ✔
(v) t² − 15
= (t − √15)(t + √15)
Zeroes: √15, −√15
Sum = 0 ✔
Product = −15 ✔
(vi) 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 ✔
Question 2: Form quadratic polynomial with given sum and product
Formula: x² − (Sum)x + Product
(i) 1/4, −1
Sum = −3/4
Product = −1/4
Polynomial: x² + (3/4)x − 1/4
Multiplying by 4:
4x² + 3x − 1
(ii) √2, 1/3
Sum = √2 + 1/3
Product = √2/3
Polynomial: x² − (√2 + 1/3)x + √2/3
(iii) 0, √5
Sum = √5
Product = 0
Polynomial: x² − √5x
(iv) 1, 1
Sum = 2
Product = 1
Polynomial: x² − 2x + 1
(v) −1/4, 1/4
Sum = 0
Product = −1/16
Polynomial: x² − 1/16
Multiplying by 16:
16x² − 1
(vi) 4, 1
Sum = 5
Product = 4
Polynomial: x² − 5x + 4
Important Concepts Used
- Factorisation of Quadratic Polynomials
- Sum and Product of Zeroes Formula
- Verification using coefficients
- Forming polynomial from given zeroes