NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.2

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.2 are part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.2.

• Polynomials Class 10 Ex 2.1
• Polynomials Class 10 Ex 2.2
• Polynomials Class 10 Ex 2.3
• Polynomials Class 10 Ex 2.4

Board	CBSE
Textbook	NCERT
Class	Class 10
Subject	Maths
Chapter	Chapter 2
	Polynomials
Exercise	Ex 2.2
Number of Questions Solved	2
Category	NCERT Solutions

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.2

Question 1.
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and their coefficients:
(i) x² – 2x – 8
(ii) 4s² – 4s + 1
(iii) 6x² – 3 – 7x
(iv) 4u² + 8u
(v) t² – 15
(vi) 3x² – x – 4
Solution:
(i) x² – 2x – 8 = x² – 4x + 2x – 8
= x(x – 4) + 2(x – 4)
= (x + 2) (x – 4)
Either x + 2 = 0 or x – 4 = 0
⇒  x = -2 or x = 4
Hence, zeroes of this polynomial are -2 and 4.
Verification:
Sum of the zeroes = (-2) + (4) = 2
=  = 
Product of zeroes = (-2) (4) = -8 =  
=  
Hence verified.

(ii) 4s² – 4s + 1 = (2s – l)² = (2s – l)(2s – 1)
Either 2s – 1 = 0 or 2s – 1 = 0
i.e. , s =  ,
Hence, the two Zeroes are and
Verification:

Hence verified.

(iii) 6x² – 3 – 7x = 6x² – 7x – 3
= 6x² – 9x + 2x – 3
= 3x (2x – 3) + 1(2x – 3)
= (2x – 3) (3x + 1)
Either 2x – 3 = 0 or 3x+1 = 0

Hence verified.

(iv) 4u² + 8u  ⇒  4u(u + 2)
Either 4u = 0 or u + 2 = 0
⇒ u = 0 or u = -2
Hence, the two zeroes are 0 and -2.
Verification:
Sum of the zeroes = 0 + (-2) = -2
=  = 
Product of zeroes = 0 x (-2) = 0 =  
Hence verified.

(v) t² – 15 = t² – ()²
= (t + () (t- ()
Either t + ( = 0 or t – ( = 0
⇒ t = -( or t = (
Hence, the two zeroes are -( and + .
Verification:
Sum of the zeroes = -( +  = 0
= 
Product of zeroes = – x  = -15
= 
Hence verified.

(vi) 3x² – x – 4 = 3x² – 4x + 3x – 4
=  x(3x – 4) + l(3x 4)
= (x + 1) (3x – 4)
Either x + 1 = 0 or 3x-4 = 0
⇒  x = -1 or x =  
Verification:
Sum of the zeroes = -1 +  =   =  
Product of zeroes = -1 x  =   =  
Hence verified.

Question 2.
Find a quadratic polynomial each with the given numbers as the sum and product of zeroes respectively:

Solution:
(i) Let the zeroes of polynomial be α and β.
Then, α + β = and αβ = -1
∴ Required polynomial is given by,
x² – (α + β)x + αβ = x² – x + (-1)
= x² – x – 1
= 4x² – x – 4

(ii) Let the zeroes of polynomial be α and β.
Then, α + β= √2 and αβ =
∴  Required polynomial is:
x² – (α + β)x + αβ = x² – √2x +
= 3x² – 3√2x + 1

(iii) Let the zeroes of the polynomial be α and β.
Then, α + β = 0 and αβ = √5
∴ Required polynomial
= x² – (α + β)x + αβ
= x²– 0 x x + √5 = x² + √5

(iv) Let the zeroes of the polynomial be α and β.
Then, α + β = 1 and αβ = 1.
∴  Required polynomial
= x² – (α + β)x + αβ
= x² – x + 1

(v) Let the zeroes of the polynomial be α and β.
Then, α + β = – and αβ = 
∴ Required polynomial
= x² – (α + β)x + αβ
= x² – (- ) + 
=  4x² + x + 1 = 0

(vi) Let the zeroes of the polynomial be α and β.
Then, α + β = 4 and αβ = 1.
∴ Required polynomial = x² -(α + β)x + αβ
= x² – 4x + 1

 

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