Tiêu đề Class 9 Mathematics Chapter 2 Polynomials.pdf ✅

Polynomials DPP-01 [Topic: Polynomials in One Variable] Very Short Answer Type Questions 1. Which of the following expressions are polynomials in one variable and which are not? State reason for your answers. (i) xx3 + xx (ii) xx + 2 xx + 3 (iii) √3xx + 1 (iv) aa10 − bb5 + cc (v) 2�yy + 3yy 2. Write the degree of each of the following polynomials: (i) xx3 − 3xx2 + 1 (ii) √2tt − 3 (iii) yy2 + 4yy (iv) 2 − yy2 − yy3 + 2yy8 3. Give an example of trinomial polynomial of degree 27. 4. Classify as linear, quadratic and cubic polynomial, (i) ss2 (ii) yy − yy2 + 1 (iii) 1 − xx2 (iv) 3 − 2xx − xx3 (v) 4tt + 3 (vi) √2xx − xx2 + 1 √3 xx3 5. Write the degree of a zero polynomial. 6. Write the degree of the polynomial pp(xx) = 4. 7. Find the degree of the polynomial: 2 − yy2 − yy3 + 2yy7. 8. Evaluate the degree of the polynomial: (yy3 − 2)(yy2 + 11) 9. Determine the degree of the following polynomials: (i) (xx − 1)(xx − 2xx2 + 3) (ii) yy3(1 − yy4) 10. Find the coefficient of xx3 in the polynomial; pp(xx) = 6xx4 − √3xx3 − 5 3 11. Find the coefficient of xx2 in (3xx2 − 5)(4 + 4xx2).
Polynomials DPP-02 [Topic: Zeroes of a Polynomial] Very Short Answer Type Questions 1. Find the value of the polynomial 5xx2 − 3xx + 7 at: (i) xx = 1 (ii) xx = −1 (iii) 0 (iv) -2 2. Find the value of the polynomial; pp(zz) = 3zz2 − 4zz + √17, when zz = 3. 3. What is the maximum number of zeroes in a cubic polynomial? 4. What is the value of polynomial 5xx − 4xx2 + 3 at xx = 1 2 ? 5. If pp(xx) = 1 3 xx3 − 2 3 xx2 + 5xx + 7, then evaluate pp(3). 6. Find zero of the polynomialpp(xx) = cc + dd 7. Find the zeroes of polynomial in each of the following: (i) pp(xx) = xx − 5 (ii) gg(xx) = 2 − 8xx (iii) qq(xx) = 2xx − 7 (iv) h(xx) = 2xx 8. Verify whether the following are zeroes of the polynomial, indicate against them. (i) xx + 2; xx = −2 (ii) xx2 − 2xx; xx = 0,2 (iii) 3xx3 − 2xx2 − xx; xx = −1 (iv) xx3 − 3√3; xx = √3 (v) xx2 − 2xx + 1; xx = 1 (vi) xx3 − 6xx2 + 11xx − 6; xx = 1,3 Short Answer Type Questions-I 9. If -4 is a zero of the polynomial: pp(xx) = xx2 + 11xx + kk, then find the value of kk. 10. Find the value of kk, if xx = 2 is a zero of pp(xx) = xx2 + kk + 2kk. 11. If pp(xx) = xx3 − xx2 + xx + 1, then find the value of pp(−1)+pp(1) 2 12. If xx = 2 is a root of the polynomial: ff(xx) = 2xx2 − 3xx + 7aa, find the value of aa. 13. If pp(xx) = xx3 − √3xx2 + 2xx − 5. Find pp(3√3). Short Answer Type Questions-II
14. If xx = 2 and xx = 0 are roots of the polynomial ff(xx) = 2xx3 − 5xx2 + aa + bb, find the value of aa and bb. 15. Find the value of aa and bb, if xx = 0 and xx = −1 are the roots of the polynomial: ff(xx) = 2xx3 − 3xx2 + aa + bb. 16. If pp(xx) = xx2 − 4xx + 3, evaluate: pp(2) − pp(−1) + pp � 1 2 �