NCERT Solutions for Class 10 Maths Chapter 2 Polynomials Ex 2.2

NCERT Solutions for Class 10 Maths Chapter 2 Ex 2.2 is a part of NCERT Solutions for Class 10 Maths. Here we have given NCERT Solutions for Chapter 2 Polynomial Class 10 Ex 2.2.

Board CBSE
Textbook NCERT
Class Class 10
Subject Maths
Chapter Chapter 2
Chapter Name 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

Page No: 33

Question 1. Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
(i) x2 – 2x – 8
(ii) 4s2 – 4s + 1
(iii) 6x2 – 3 – 7x
(iv) 4u2 + 8u
(v) t2 – 15
(vi) 3x2 – x – 4

Solution:

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials 2
So, the zeroes of x² – 2x – 8 are 4 and -2.
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Concept insight: The zero of a polynomial is the value of the variable which, when substituted into the polynomial, becomes 0. When a quadratic polynomial is made equal to 0, the values of the variables obtained are zeroes of that polynomial. The relationship between the zeroes of a quadratic polynomial and its coefficients is very important. Also, when verifying the above relations, be careful about the signs of the coefficients.

Question 2. Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
(i) 1/4, -1
(ii) √2, 1/3
(iii) 0, √5
(iv) 1,1
(v) -1/4,1/4
(vi) 4,1

Solution:
(i)    Let the required polynomial be  ax² + bx + c, and let its zeroes α and β

NCERT Solutions for Class 10 Maths Chapter 2 Polynomials 9
If a = 4k, then b = -k, c = -4k  Therefore, the quadratic polynomial is k(4 x 2 – x – 4), where k is a real number .
(ii)     Let the polynomial be  ax² + bx + c, and let its zeroes be α and β
NCERT Solutions for Class 10 Maths Chapter 2 Polynomials 10
(iii)    Let the polynomial be  ax² + bx + c, and let its zeroes be α and β
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(iv)    Let the polynomial be  ax² + bx + c, and let its zeroes be α and β
Therefore, the quadratic polynomial is k(x² – x + 1), where k is a real number.
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(v)    Let the polynomial be ax² + bx + c, and its zeroes be α and β
Therefore, the quadratic polynomial is k(4x² + x + 1),where k is a real number .
(vi)    Let the polynomial be ax² + bx + c.
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Therefore, the quadratic polynomial is k(x² – 4x + 1), where k is a real number.

Concept insight: Since the sum and multiplication of zero gives a relation of 2 between the three unknowns, we assign one value to the variable a and obtain the other value.
Alternatively, if the sum and product of the zeroes of a quadratic polynomial is given, the polynomial is given, where k is a constant. And the simplest polynomial would be the one in which k = 1.

 

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