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. Equation

  2. Equation

  3. Equation

  4. Equation

  5. Equation

  6. Equation

  7. Equation

  8. Equation

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 Equation is a zero of polynomial Equation

    Then, Equation should be 0

    Equation

    Equation

    Therefore, Equation is a zero of polynomial Equation

  2. If Equation is a zero of polynomial Equation

    Then, Equation should be 0

    Equation

    Equation

    Therefore, Equation is not a zero of polynomial Equation

  3. If Equation are the zeros of polynomial Equation

    Then, Equation should be 0

    Equation

    Equation

    Therefore, Equation ae zeros of polynomial Equation

  4. If Equation are zeros of polynomial Equation

    Then, Equation should be 0

    Equation

    Equation

    Therefore, Equation are zeros of polynomial Equation

  5. If Equation is a zero of polynomial Equation

    Then, Equation should be 0

    Equation

    Therefore, Equation is a zero of polynomial Equation

  6. If Equation is a zero of polynomial Equation

    Then, Equation should be 0

    Equation

    Equation

    Therefore, Equation is a zero of polynomial Equation

  7. If Equation are zeros of polynomial Equation

    Then, Equation should be 0

    Equation

    Equation

    Therefore, Equation is a zero of polynomial Equation

    But Equation is not a zero of this polynomial

  8. If Equation is a zero of polynomial Equation

    Then, Equation should be 0

    Equation

    Therefore, Equation is not a zero of polynomial Equation

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

  1. Equation

  2. Equation

  3. Equation

  4. Equation

  5. Equation

  6. Equation

  7. Equation

Solution:

Polynomials for each type and their roots

Types of Polynomials and Their Roots

Polynomials for each type and their roots

  1. Equation

    The value of x for which the polynomial becomes zero, i.e. Equation are known as “zeros” of the polynomial.

    We have to find x for which, Equation

    Equation

    Therefore, Equation is a zero of polynomial Equation

  2. Equation The value of x for which the polynomial becomes zero, i.e. Equation are known as “zeros” of the polynomial.

    Equation

    Equation

    Therefore, Equation is a zero of polynomial Equation

  3. Equation The value of x for which the polynomial becomes zero, i.e. Equation are known as “zeros” of the polynomial.

    We have to find x for which, Equation

    Equation

    Equation

    Therefore, Equation is a zero of polynomial Equation

  4. Equation The value of x for which the polynomial becomes zero, i.e. Equation are known as “zeros” of the polynomial.

    We have to find x for which, Equation

    Equation

    Equation

    Therefore, Equation is a zero of polynomial Equation

  5. Equation The value of x for which the polynomial becomes zero, i.e. Equation are known as “zeros” of the polynomial.

    We have to find x for which, Equation

    Equation

    Therefore, Equation is a zero of polynomial Equation

  6. Equation The value of x for which the polynomial becomes zero, i.e. Equation are known as “zeros” of the polynomial.

    We have to find x for which, Equation

    Equation

    Therefore, Equation is a zero of polynomial Equation

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