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NCERT Solutions for Class 9th Mathematics

 

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Chapter 2. Polynomials

Exercise 2.2

 

 

 

2. Polynomials


Exercise 2.2

Q1. Find the value of the polynomial 5x – 4x2 + 3 at

(i) x = 0 (ii) x = –1 (iii) x = 2

Solution:

(i) p(x) = 5x - 4x2 + 3

The value of the polynomial p(x) at x = 0 is given by

P(0) = 5(0) - 4(0)2 + 3

       = 0 - 0 + 3

       = 3

(ii) p(x) = 5x - 4x2 + 3

The value of the polynomial p(x) at x = 1 is given by

P(1) = 5(1) - 4(1)2 + 3

        = 5 - 4 + 3

        = 4

(iii) p(x) = 5x - 4x2 + 3

The value of the polynomial p(x) at x = 2 is given by

P(2) = 5(2) - 4(2)2 + 3

       = 10 -16 + 3

       = - 9

Q2.Find p(0), p(1) and p(2) for each of the following polynomials:

(i)  p(y) = y2 – y + 1

(ii) p(t) = 2 + t + 2t 2 – t 3

(iii) p(x) = x3

(iv) p(x) = (x – 1) (x + 1)

Solution:

(i) p(y) = y2 - y + 1

    P(0) = (0)2- 0 + 1

            =1

  P(1) = (1)2- 1 + 1

          = 1 - 1 + 1

          = 1

P(2) = (2)2- 2 + 1 = 4 - 2 + 1 = 3

(ii) p(t) = 2 + t + 2t2- t3

     P(0) = 2 + 0 + 2(0)2- (0)3

            =2

   P(1) = 2 + 1 + 2(1)2 - (1)3

            = 4

   P(2) = 2 + 2 + 2(2)2- (2)3

            = 4 + 8 - 8

            = 4

(iii) p(x) = x3

       P(0)=(0)3 =0

       P(1)=(1)3 =1

       P(2)=(2)3=8

(iv)p(x) = (x – 1) (x + 1)

       P(0)= (0-1) (0+1)=(-1) (1) =-1

       P(1)= (1-1) (1+1) =0(1)  =0

       P(2)= (2-1) (2+1)=1(3)  =3 

Q3. Verify whether the following are zeroes of the polynomial, indicated against them.

Solution:  

Q4. Find the zero of the polynomial in each of the following cases: 

(i)  P(x) = x + 5                                

(ii) P(x) = x 5                           

(iii) Px) = 2x + 5                              

(iv) P(x) = 3x 2                          

(v) P(x) = 3x                                    

(vi) P(x) = ax, a  0

Solution (i) :

(i)   P(x) = x + 5

      x + 5 = 0

     ⇒ x = - 5 

The zero of the polynomial is - 5. 

 Solution (ii) :

 (ii) P(x) = x  5

       x  5  = 0

     ⇒ x = 5

 The zero of the polynomial is  5.

 

The zero of the polynomial is - 5/2.

(iv)  P(x) = 3x - 2

       3x - 2 = 0

              

The zero of the polynomial is 2/3.

  

 

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