NCRT 9th class chapter=2 polynomials exercise 2.1

                  Exercise 2.1

Question :1)

Which of the following expressions are polynomials in one variable and which are not?

State reasons for vour answer.

 i)   4x²-3x +7

  Answer: 

      In equation 4x²-3x +7 , the one variable 'x' is given and has a power in whole number  , so the above equation is in one variable .

ii)   y²+√2

      solution 

     In equation y²+√2 , the one variable 'x' is 

      given , so the above equation is in one 

      variable .

iii) 3√t+√2 t

       Answer:

      In equation 3√t+t√2 , the power of √t =t^1/2      so the power is in fraction thats why we            can say that above expression  is not in one             variable .

iv) y+2/y

Answer :

     In equation y+2/y , the power of y is (-1).

     it is not in whole number i.e the above                 equation is not in one variable .

  

v)  x10+  y3 + t50

Answer:

     In equation x10+  y3 + t50, every variable is 

     in whole number but there is different                   variable

    (x,y,z) is given . so the above expression is          not in one variable.

 Question : 2 )

Write the coefficients of x2 in each of the following

(i) 2 + x2 + x
(ii) 2 – x2 + x3
(iii)  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  + x.
       The coefficient of x2 is .
(iv) The given polynomial is √2 x – 1.
       The coefficient of x2 is 0.

 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                    x35 -4.
(ii)   A monomial of degree 100 can be              5x100.

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 variable t is 1. So, the degree of the polynomial is 1.
(iv) Since, 3 = 3x° [∵ x°=1]
So, the degree of the polynomial is 0.

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 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.