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Class 9 Maths NCERT Solution for Polynomial part 1




In this page we have NCERT book Solutions for Class 9th Maths:Polynomial for EXERCISE 1 . Hope you like them and do not forget to like , social share and comment at the end of the page.

Question 1:

Which of the following expressions are polynomials in one variable and which are

not? State reasons for your answer.

4x2– 3x + 7

y2 + √2

3 √t + t√ 2

 y + 2/y

x10 + y3 + t50

 

Solution:

(i) 4x2– 3x + 7

Yes, this expression is a polynomial in one variable x.

(ii) y2 + √2

 

Yes, this expression is a polynomial in one variable y.

(iii) 3 √t + t√ 2

 No. It can be observed that the exponent of variable t in term 3 √t is 1/2, which is not a whole number. Therefore, this expression is not a polynomial.

(iv) y+2/y  

No. It can be observed that the exponent of variable y in term 2/y is -1 which is not a whole number. Therefore, this expression is not a polynomial.

(v) x10 + y3 + t50

 

No. It can be observed that this expression is a polynomial in 3 variables x, y, and t. Therefore, it is not a polynomial in one variable.

 

Question 2.

Write the coefficients of x2 in each of the following:

  1. 2 + x2 + x
  2. 2 – x2 + x3
  3. (π/2)x2 + x
  4. √ 2  x −1

Solution:

(i) 2+x2+x

 Coefficient of x2 is 1.

 (ii)  2−x2+x3

 Coefficient of x2 is -1.

(iii) (π/2)x2 + x

Coefficient of x2 is (π/2)

(iv) √ 2  x −1

 There is no term consisting of x2. Therefore, 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:

Degree of a polynomial is the highest power of variable in the polynomial.
Binomial has two terms in it. So binomial of degree 35 can be written as x35 + 1. 

Monomial has only one term in it. So monomial of degree 100 can be written as x100

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) This is a polynomial in variable x and the highest power of variable x is 3 Therefore, the degree of this polynomial is 3.

(ii)This is a polynomial in variable y and the highest power of variable y is 2. Therefore, the degree of this polynomial is 2.

(iii) This is a polynomial in variable t and the highest power of variable t is 1. Therefore, the degree of this polynomial is 1.

(iv)This is a constant polynomial. Degree of a constant polynomial is always 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)       2 + x2 + x  is a quadratic polynomial as its degree is 2.

(ii)      x – x3 is a cubic polynomial as  its degree is 3.

(iii)     y + y2 + 4  is a quadratic polynomial as its degree is 2.

(iv)     1 + x is a linear polynomial as its degree is 1.

(v)      3t is a linear polynomial as its degree is 1.

(vi)     r2 is a quadratic polynomial as its degree is 2.

(vii)   7x3 is a cubic polynomial as its degree is 3.

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