NCERT Solutions for Class 10 Maths Exercise 2.2 Chapter 2 Polynomials – FREE PDF Download
NCERT Class 10 Maths Ch 2 is one of the most important ones in the NCERT syllabus. Duly following NCERT Solutions for Class 10 Maths Chapter 2 ensures you that there will be no hindrance when you opt for more advanced branches of Maths. This is where CoolGyan comes in. Our free Class 10 Polynomials solutions will help you understand the chapter thoroughly.
NCERT Solutions for Class 10 Maths Chapter 2 – Polynomials
1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeros and the coefficients.
(i) 
(ii) 
(iii) 
(iv) 
(v) 
(vi) 
Comparing given polynomial with general form of quadratic polynomial 
,
We get a = 1, b = -2 and c = -8
We have,
= x(x−4)+2(x−4) = (x−4)(x+2)
Equating this equal to 0 will find values of 2 zeroes of this polynomial.
(x−4)(x+2) = 0
⇒ x = 4, −2 are two zeroes.
Sum of zeroes = 4 + (– 2) = 2 =
=> 
= 
Product of zeroes = 4 × (−2) = −8
= 
(ii) 
Here, a = 4, b = -4 and c = 1
We have,
=
=2s(2s−1)−1(2s−1)
= (2s−1)(2s−1)
Equating this equal to 0 will find values of 2 zeroes of this polynomial.
⇒ (2s−1)(2s−1) = 0
⇒ s = 
Therefore, two zeroes of this polynomial are
Sum of zeroes = 
= 1 = 
=
Product of Zeroes = 
(iii) 
⇒⇒ 6x2−7x−36×2−7x−3
Here, a = 6, b = -7 and c = -3
We have, 6x2−7x−36×2−7x−3
= 3x(2x−3)+1(2x−3) = (2x−3)(3x+1)
Equating this equal to 0 will find values of 2 zeroes of this polynomial.
⇒ (2x−3)(3x+1) = 0
⇒ x = 
Therefore, two zeroes of this polynomial are
Sum of zeroes = 
Product of Zeroes = 
(iv) 
Here, a = 4, b = 8 and c = 0
Equating this equal to 0 will find values of 2 zeroes of this polynomial.
⇒ 4u(u+2) = 0
⇒ u = 0,−2
Therefore, two zeroes of this polynomial are 0, −2
Sum of zeroes = 0−2 = −2
= 
=
Product of Zeroes 
= 0
= 
(v) 
Here, a = 1, b = 0 and c = -15
We have, ⇒ 
⇒ t = 
Therefore, two zeroes of this polynomial are 
Sum of zeroes = 
Product of Zeroes = 
(vi) 
Here, a = 3, b = -1 and c = -4
We have, = 
= x(3x−4)+1(3x−4) = (3x−4)(x+1)
Equating this equal to 0 will find values of 2 zeroes of this polynomial.
⇒ (3x−4)(x+1) = 0
⇒ x = 
Therefore, two zeroes of this polynomial are
Sum of zeroes = 
Product of Zeroes = 
2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
(i) 
, −1
(ii) 
, 13
(iii) 0, 
(iv) 1, 1
(v) 
(vi) 4, 1
, −1 Let quadratic polynomial be
Let α and β are two zeroes of above quadratic polynomial.
α+β = = 
α × β = -1 
= 
On comparing, we get
Putting the values of a, b and c in quadratic polynomial , we get
Quadratic polynomial which satisfies above conditions = 
(ii) 
Let quadratic polynomial be
Let α and β be two zeros of above quadratic polynomial.
α+β = 
=
α × β = 
which is equal to
On comparing, we get
Putting the values of a, b and c in quadratic polynomial , we get
Quadratic polynomial which satisfies above conditions = 3x2−32–√x+1.3×2−32x+1.
(iii) 0,
Let quadratic polynomial be 
Let α and β be two zeros of above quadratic polynomial.
α+β = 0 
=
α 
β = 
=
On comparing, we get
Putting the values of a, b and c in quadratic polynomial , we get
Quadratic polynomial which satisfies above conditions 
(iv) 1, 1
Let quadratic polynomial be
Let α and β be two zeros of above quadratic polynomial.
α+β = 1 
=
α β = 1 
=
On comparing, we get
Putting the values of a, b and c in quadratic polynomial , we get
Quadratic polynomial which satisfies above conditions = 
(v)
Let quadratic polynomial be
Let α and β be two zeros of above quadratic polynomial.
α+β = 
=
α β = =
On comparing, we get
Putting the values of a, b and c in quadratic polynomial , we get
Quadratic polynomial which satisfies above conditions = 
(vi) 4, 1
Let quadratic polynomial be
Let α and β be two zeros of above quadratic polynomial.
α+β = 4 
=
α × β = 1 =
On comparing, we get
Putting the values of a, b and c in quadratic polynomial , we get
Quadratic polynomial which satisfies above conditions 
