NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1 is a part of NCERT Solutions for Class 9 Maths. Here we have given the NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1.
Polynomials
Introduction
Polynomials In One Variable
Zeroes Of A Polynomial
Remainder Theorem
Factorisation Of Polynomials
Algebraic Identities
Summary
NCERT Solutions for Class 9 Maths Chapter 2 Polynomials Ex 2.1
Post Contents
Exercise 1.1 Page: 6
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+ \(\frac { 2 }{ y }\) (v) x10+ y3+t50
Solution:
(i) We have 4x2 – 3x + 7 = 4x2 – 3x + 7x0.
It is a polynomial in one variable i.e. x
Because every exponent of x is a whole number.
(ii) We have y2 + √2 = y2 + √2y0 .
It is a polynomial in one variable, i.e., y
Because every exponent of y is a whole number.
(iii) We have 3 √t + t√2 = 3 √t1/2 + √2.t
It is not a polynomial, because one of the exponents of t is \(\frac { 1 }{ 2 }\),
which is not a whole number.
(iv) We have y + \(y+\frac { 2 }{ y }\) = 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) We have x10+ y3 + t50
Here, the exponent of each variable is a whole number, but x10+ y3 + t50 is a polynomial in x, y and t, that is, in three variables.
Hence it is not a polynomial with 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) \(\frac { \pi }{ 2 }\) 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 \(\frac { \pi }{ 2 } { x }^{ 2 }\) + x.
The coefficient of x2 is \(\frac { \pi }{ 2 }\) .
(iv) The given polynomial is √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) Abmomial of degree 35 can be 3x35 -4.
(ii) A monomial of degree 100 can be √2y100.
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.
Hence, the power of the polynomial is 3.
(ii) The given polynomial is 4- y2. Highest
The power of the variable y is 2.
Hence, the power of the polynomial is 2.
(iii) The given polynomial is 5t – √7 . The highest power of the variable t is 1. Hence, the power of the polynomial is 1.
(iv) Since,3 = 3x° [∵ x°=1]
So the power 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 power of x2 + x is 2. Hence, it is a quadratic polynomial.
(ii) The power of x – x3 is 3. Hence, it is a cubic polynomial.
(iii) The power of y + y2 + 4 is 2. Hence, it is a quadratic polynomial.
(iv) The power of 1 + x is 1. Hence it is a linear polynomial.
(v) The power of 3t is 1. Hence, it is a linear polynomial.
(vi) The power of r2 is 2. Hence, it is a quadratic polynomial.
(vii) The power of 7x3 is 3. Hence, it is a cubic polynomial.
