CLASS 10 MATHEMATICS – WORKSHEET
Chapter 2: Polynomials
Name: ______________________________ Class/Section: __________ Date: ______________
Instructions: Attempt all questions. Show necessary steps. Use the factor theorem and relationship between
zeroes and coefficients wherever required.
A. Very Short Answer Questions
1. 1. Find the degree of the polynomial 5x³ − 2x² + 7.
2. 2. Find the zero of the linear polynomial 3x − 12.
3. 3. If one zero of p(x) = x² − 5x + 6 is 2, find the other zero.
4. 4. State the relationship between the zeroes α, β of ax² + bx + c and its coefficients.
5. 5. How many zeroes can a non-zero quadratic polynomial have at maximum?
B. Find the Zeroes
6. 6. Find the zeroes of x² − 7x + 12 and verify the relationship between zeroes and coefficients.
7. 7. Find the zeroes of 2x² − 5x − 3.
8. 8. Find the zeroes of 3x² + 2x − 8.
9. 9. Find the zeroes of 4x² − 4x − 15.
C. Form a Polynomial
10. 10. Find a quadratic polynomial whose zeroes are 3 and −5.
11. 11. Find a quadratic polynomial whose zeroes are 2/3 and −4.
12. 12. Find a quadratic polynomial whose sum of zeroes is 7 and product of zeroes is 10.
13. 13. If the zeroes of a quadratic polynomial are −2 and 5, write the polynomial with leading coefficient 2.
D. HOTS / Application
14. 14. If α and β are the zeroes of 2x² − 7x + 3, find α² + β².
15. 15. If α and β are the zeroes of x² − 6x + 4, find 1/α + 1/β.
16. 16. If one zero of 2x² + kx + 6 is 2, find k and the other zero.
17. 17. Find the value of k if the polynomial x² + (k − 3)x + k has equal zeroes.
18. 18. If α and β are the zeroes of x² − 4x + 1, form a polynomial whose zeroes are α² and β².
E. Graphical / Conceptual
19. 19. What does the number of zeroes of a polynomial represent graphically?
20. 20. A quadratic polynomial has its graph touching the x-axis at exactly one point. How many distinct zeroes
does it have?
21. 21. Can a quadratic polynomial have no real zeroes? Give one example.
22. 22. For p(x) = x² − 9, state the zeroes and describe where its graph intersects the x-axis.
Challenge Question
23. If α and β are the zeroes of x² − 5x + 3, find the value of (α/β) + (β/α).
Chapter 2: Polynomials
Name: ______________________________ Class/Section: __________ Date: ______________
Instructions: Attempt all questions. Show necessary steps. Use the factor theorem and relationship between
zeroes and coefficients wherever required.
A. Very Short Answer Questions
1. 1. Find the degree of the polynomial 5x³ − 2x² + 7.
2. 2. Find the zero of the linear polynomial 3x − 12.
3. 3. If one zero of p(x) = x² − 5x + 6 is 2, find the other zero.
4. 4. State the relationship between the zeroes α, β of ax² + bx + c and its coefficients.
5. 5. How many zeroes can a non-zero quadratic polynomial have at maximum?
B. Find the Zeroes
6. 6. Find the zeroes of x² − 7x + 12 and verify the relationship between zeroes and coefficients.
7. 7. Find the zeroes of 2x² − 5x − 3.
8. 8. Find the zeroes of 3x² + 2x − 8.
9. 9. Find the zeroes of 4x² − 4x − 15.
C. Form a Polynomial
10. 10. Find a quadratic polynomial whose zeroes are 3 and −5.
11. 11. Find a quadratic polynomial whose zeroes are 2/3 and −4.
12. 12. Find a quadratic polynomial whose sum of zeroes is 7 and product of zeroes is 10.
13. 13. If the zeroes of a quadratic polynomial are −2 and 5, write the polynomial with leading coefficient 2.
D. HOTS / Application
14. 14. If α and β are the zeroes of 2x² − 7x + 3, find α² + β².
15. 15. If α and β are the zeroes of x² − 6x + 4, find 1/α + 1/β.
16. 16. If one zero of 2x² + kx + 6 is 2, find k and the other zero.
17. 17. Find the value of k if the polynomial x² + (k − 3)x + k has equal zeroes.
18. 18. If α and β are the zeroes of x² − 4x + 1, form a polynomial whose zeroes are α² and β².
E. Graphical / Conceptual
19. 19. What does the number of zeroes of a polynomial represent graphically?
20. 20. A quadratic polynomial has its graph touching the x-axis at exactly one point. How many distinct zeroes
does it have?
21. 21. Can a quadratic polynomial have no real zeroes? Give one example.
22. 22. For p(x) = x² − 9, state the zeroes and describe where its graph intersects the x-axis.
Challenge Question
23. If α and β are the zeroes of x² − 5x + 3, find the value of (α/β) + (β/α).
