NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1

NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1 are the part of NCERT Solutions for Class 9 Maths. Here you can find the NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1.



Ex 2.1 Class 9 Maths Question 1.
Which of the following expressions are polynomials in one variable and which are not? State reasons for your answer.
(i) 4x2 – 3x + 7              (ii) y2 + √2               (iii) 3√t + t√2
(iv) y + 2/y                    (v) x10 + y3 + t50

Solution:
(i)
4x2 – 3x + 7

It is a polynomial in one variable, i.e., x, because each exponent of x is a whole number.

(ii) y2 + √2
It is a polynomial in one variable, i.e., y, because each exponent of y is a whole number.

(iii) 3√t + t√2 = 3(t)1/2 + √2.t
It is not a polynomial, because one of the exponents of t is 1/2, which is not a whole number.

(iv) y + 2/y = y + 2.y-1
It is not a polynomial, because one of the exponents of y is -1, which is not a whole number.

(v) x10 + y+ t50
Here, exponent of every variable is a whole number, but x10 + y3 + t50 is a polynomial in three variables, i.e., in x, y and t.
So, it is not a polynomial in one variable.

 

Ex 2.1 Class 9 Maths Question 2.
Write the coefficients of x2 in each of the following:
(i) 2 + x2 + x                            (ii) 2 – x2 + x3
(iii) π/2 . x2 + x                       (iv) √2 x – 1

Solution:
(i)
The given polynomial is 2 + x2 + x.
The coefficient of x2 is 1.
(ii) The given polynomial is 2 – x2 + x3.
The coefficient of x2 is -1.
(iii) The given polynomial is π/2 . x2 + x.
The coefficient of x2 is π/2.
(iv) The given polynomial is √2 x – 1. It can be written as 0.x2 + √2 x – 1.
The coefficient of x2 is 0.

 

Ex 2.1 Class 9 Maths Question 3.
Give one example each of a binomial of degree 35, and of a monomial of degree 100.

Solution:
(i)
A binomial of degree 35 can be written as 2x35 + 5.
(ii) A monomial of degree 100 can be written as 4y100 – 3.

 

Ex 2.1 Class 9 Maths Question 4.
Write the degree of each of the following polynomials.
(i) 5x3 + 4x2 + 7x                       (ii) 4 – y2
(iii) 5t – √7                                (iv) 3

Solution:
(i)
The given polynomial is 5x3 + 4x2 + 7x.
The highest power of the variable x is 3.
So, the degree of the polynomial is 3.
(ii) The given polynomial is 4 – y2.

The highest power of the variable y is 2.
So, the degree of the polynomial is 2.
(iii) The given polynomial is 5t – √7.

The highest power of the variable t is 1.

So, the degree of the polynomial is 1.
(iv) The given polynomial is 3.

Since, 3 can be written as 3x0. That is 3 = 3x0      [ x0 = 1]
So, the degree of the polynomial is 0.

 

Ex 2.1 Class 9 Maths Question 5.
Classify the following as linear, quadratic and cubic polynomials:
(i) x2 + x                                    (ii) x – x3                             (iii) y + y2+ 4                                    (iv) 1 + x                                   (v) 3t                                 (vi) r2
(vii) 7x3

Solution:
(i)
The highest degree of x2 + x is 2. So, it is a quadratic polynomial.
(ii) The highest degree of x – x3 is 3. So, it is a cubic polynomial.

(iii) The highest degree of y + y2 + 4 is 2. So, it is a quadratic polynomial.

(iv) The highest degree of 1 + x is 1. So, it is a linear polynomial.
(v) The highest degree of 3t is 1. So, it is a linear polynomial.
(vi) The highest degree of r2 is 2. So, it is a quadratic polynomial.
(vii) The highest degree of 7x3 is 3. So, it is a cubic polynomial.

 


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