NCERT Class 9 Solutions: Polynomials (Chapter 2) Exercise 2.2 – Part 2

Q-3 Verify whether the following are zeroes of the polynomial, indicated against them.

  1. p(x)=3x+1,x=13

  2. p(x)=5xπ,x=45

  3. p(x)=x21,x=1,1

  4. p(x)=(x+1)(x2),x=1,2

  5. p(x)=x2,x=0

  6. p(x)=ix+m,x=ml

  7. p(x)=3x21,x=13,23

  8. p(x)=2x+1,x=12

Solution:

Zero of a polynomial are the points where its value becomes zero.

Value of polynomial is zero at its root

Understanding Zeros of Polynomials

Value of polynomial is zero at its root

  1. If x=13 is a zero of polynomial p(x)=3x+1

    Then, p(13) should be 0

    p(13)=3(13)+1

    p(13)=1+1=0

    Therefore, x=13 is a zero of polynomial p(x)=3x+1

  2. If x=45 is a zero of polynomial p(x)=5xπ

    Then, p(45) should be 0

    p(45)=5(45)π

    p(45)=4π

    Therefore, x=45 is not a zero of polynomial p(x)=5xπ

  3. If x=1andx=1 are the zeros of polynomial p(x)=x21

    Then, p(1)andp(1) should be 0

    p(1)=(1)21=0

    p(1)=(1)21=0

    Therefore, x=1andx=1 ae zeros of polynomial p(x)=x21

  4. If x=1andx=2 are zeros of polynomial p(x)=(x+1)(x2)

    Then, p(1)andp(2) should be 0

    p(1)=(1+1)(12)=0×(3)=0

    p(2)=(2+1)(22)=3×0=0

    Therefore, x=1andx=2 are zeros of polynomial p(x)=(x+1)(x2)

  5. If x=0 is a zero of polynomial p(x)=x2

    Then, p(0) should be 0

    p(0)=(0)2=0

    Therefore, x=0 is a zero of polynomial p(x)=x2

  6. If x=ml is a zero of polynomial p(x)=lx+m

    Then, p(ml) should be 0

    p(ml)=l(ml)+m

    p(ml)=m+m=0

    Therefore, x=ml is a zero of polynomial p(x)=lx+m

  7. If x=13andx=23 are zeros of polynomial p(x)=3x21

    Then, p(13)andp(23) should be 0

    p(13)=3×(13)21=3(13)1=11=0

    p(23)=3×(23)21=3(43)1=41=3

    Therefore, x=13 is a zero of polynomial p(x)=3x2+1

    But x=23 is not a zero of this polynomial

  8. If x=12 is a zero of polynomial p(x)=2x+1

    Then, p(12) should be 0

    p(12)=2(12)+1=1+1=2

    Therefore, x=12 is not a zero of polynomial p(x)=2x+1

Q-4 Find the zero of the polynomial in each of the following cases:

  1. p(x)=x+5

  2. p(x)=x5

  3. p(x)=2x+5

  4. p(x)=3x2

  5. p(x)=3x

  6. p(x)=ax,a0

  7. p(x)=cx+d,c,c,darerealnumbers

Solution:

Polynomials for each type and their roots

Types of Polynomials and Their Roots

Polynomials for each type and their roots

  1. p(x)=x+5

    The value of x for which the polynomial becomes zero, i.e. p(x)=0 are known as “zeros” of the polynomial.

    We have to find x for which, x+5=0

    x=5

    Therefore, x=5 is a zero of polynomial p(x)=x+5

  2. p(x)=x5 The value of x for which the polynomial becomes zero, i.e. p(x)=0 are known as “zeros” of the polynomial.

    x5=0

    x=5

    Therefore, x=5 is a zero of polynomial p(x)=x5

  3. p(x)=2x+5 The value of x for which the polynomial becomes zero, i.e. p(x)=0 are known as “zeros” of the polynomial.

    We have to find x for which, 2x+5=0

    2x=5

    x=52

    Therefore, x=52 is a zero of polynomial p(x)=2x+5

  4. p(x)=3x2 The value of x for which the polynomial becomes zero, i.e. p(x)=0 are known as “zeros” of the polynomial.

    We have to find x for which, 3x2=0

    3x=2

    x=23

    Therefore, x=23 is a zero of polynomial p(x)=3x2

  5. p(x)=3x The value of x for which the polynomial becomes zero, i.e. p(x)=0 are known as “zeros” of the polynomial.

    We have to find x for which, 3x=0

    x=0

    Therefore, x=0 is a zero of polynomial p(x)=3x

  6. p(x)=cx+d The value of x for which the polynomial becomes zero, i.e. p(x)=0 are known as “zeros” of the polynomial.

    We have to find x for which, cx+d=0

    x=dc

    Therefore, x=cd is a zero of polynomial p(x)=cx+d

Explore Solutions for Mathematics

Sign In