NCERT Mathematics Class 9 Exemplar Ch 2 Polynomials Part 5 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Exercise 2.3

Q. 1. Classify the following polynomials as polynomials in one variable, two variables etc.

(i)

(ii)

(iii)

(iv)

Answer: (i) One variable (ii) One variable (iii) Three variable (iv) Two variables

Q. 2. Determine the degree of each of the following polynomials:

(i)

(ii)

(iii)

(iv)

Answer: (i) 1 (ii) 0 (iii) 5 (iv) 7

Q. 3. For the polynomial , write

(i) The degree of the polynomial

(ii) The coefficient of x3

(iii) The coefficient of x6

(iv) The constant term

Answer: (i) 6 (ii) (iii) – 1 (iv)

Q. 4. Write the coefficient of x2 in each of the following:

(i)

(ii)

(iii)

(iv)

Answer: (i) 1 (ii) 0 (iii) 3 (iv) – 16

Q. 5. Classify the following as a constant, linear, quadratic and cubic polynomials:

(i)

(ii)

(iii)

(iv)

(v) 3

(vi)

(vii)

(viii)

(ix)

(x)

Answer: Constant Polynomial: (v)

Linear Polynomials: (iii) , (vi) , (x)

Quadratic Polynomials: (iv) , (viii) , (ix)

Cubic Polynomials: (i) , (ii) , (vii)

Q. 6. Give an example of a polynomial, which is:

(i) Monomial of degree 1

(ii) Binomial of degree 20

(iii) Trinomial of degree 2

Answer: (i) (ii) (iii)

Q. 7. Find the value of the polynomial , when and also when .

Answer:

Q. 8. If , evaluate:

Answer:

Q. 9. Find for the following polynomials:

(i)

(ii)

Answer: (i)

(ii)

Q. 10. Verify whether the following are true or false:

(i) is a zero of

(ii) is a zero of

(iii) is a zero of

(iv) 0 and 2 are the zeroes of

(v) is a zero of

Answer: (i) False (ii) True (iii) False (iv) True (v) True