NCERT Solutions for Class 9 Maths Chapter-2 Polynomials Exercise 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+ 2y
(v) x10+ y3+t50
Sol. (i) We can write the equation 4x2 – 3x + 7 as
= 4x2 – 3x + 7x0
Since, x is the only variable in this equation,
It is a polynomial in one variable i.e., x
because each exponent of x is a whole number.
(ii) We have y2 + √2 = y2 + √2y0
Since, y is the only variable in this equation,
It is a polynomial in one variable i.e., y
because each exponent of y is a whole number.
(iii) We have 3√t + t√2 = 3t1/2 + √2t
because t is the only variable in this equation,
It is not a polynomial, because one of the exponents of t is 1/2,
which is not a whole number.
(iv) We have y+2y=y+2y-1
As we can see, y is the only variable in this equation,
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 every variable is a whole number, but x10+ y3 + t50 is a polynomial in x, y and t, i.e., in three variables.
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
(iv) √2 x – 1
Sol. (i) The given polynomial is 2 + x2 + x
It can be written as, 2 + (1)x2 + x
The coefficient of x2 is 1.
(ii) The given polynomial is 2 – x2 + x3
It can be written as, 2 – (1)x2 + x3
The coefficient of x2 is -1.
(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.
Sol. (i) A binomial of degree 35 can be 7x35 -2.
(ii) A monomial of degree 100 can be 3y100.
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
Sol.
(i) It is given that, 5x3 + 4x2 + 7x.
The highest power of the variable x is 3.
So, the degree of the polynomial is 3.
(ii) In polynomial 4 – y2.
The highest power of the variable y is 2.
So, the degree of the polynomial is 2.
(iii) In the given polynomial 5t – √7.
The highest power of variable t is 1.
So, the degree of the polynomial is 1.
(iv) As we know, 3 = 3x°
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
Sol. Linear polynomial: A polynomial of degree one.
Quadratic Polynomial: A polynomial of degree two.
Cubic Polynomial: A polynomial of degree three.
(i) The degree of x2 + x is 2. So, it is a quadratic polynomial.
(ii) The degree of x – x3 is 3. So, it is a cubic polynomial.
(iii) The degree of y + y2 + 4 is 2. So, it is a quadratic polynomial.
(iv) The degree of 1 + x is 1. So, it is a linear polynomial.
(v) The degree of 3t is 1. So, it is a linear polynomial.
(vi) The degree of r2 is 2. So, it is a quadratic polynomial.
(vii) The degree of 7x3 is 3. So, it is a cubic polynomial.