A quadratic polynomial has degree 2 and x² − 9 has zeroes 3 and −3, so this Class 10 sheet opens with degree and roots of a difference of squares. The answers record 5 as a value and −3 and −4 as zeroes of a quadratic.
Key Takeaways
A quadratic polynomial has degree 2 (Q1).
The zeroes of x² − 9 are 3 and −3 (Q2).
Q4 records −3 and −4 as polynomial zeroes.
Section A: Multiple Choice Questions (1 Mark Each)
Choose the correct option for each question.
1.The degree of a quadratic polynomial is
(a) 1(b) 2(c) 3(d) 0
2.The zeroes of the polynomial x² - 9 are
(a) 3 and -3(b) 9 and -9(c) 0 and 9(d) 3 and 9
3.If α and β are the zeroes of x² - 5x + 6, then α + β is
(a) 5(b) -5(c) 6(d) -6
4.The zeroes of the polynomial p(x) = x² + 7x + 12 are
(a) -3 and -4(b) 3 and 4(c) -3 and 4(d) 3 and -4
5.The graph of a polynomial cuts the x-axis at 3 distinct points. The number of real zeroes of the polynomial is
(a) 0(b) 1(c) 2(d) 3
6.For the polynomial p(x) = x² - 2x + 1, the sum and the product of the zeroes are respectively
(a) 2 and 1(b) 1 and 2(c) -2 and 1(d) 2 and -1
Section B: Short Answer Type Questions (2 Marks Each)
Show all steps clearly.
7.Find the zeroes of the polynomial x² - 4.
8.Write a quadratic polynomial whose sum of zeroes is 3 and product of zeroes is 2.
9.How many real zeroes does the polynomial p(x) = x² + 1 have?
10.Verify that 2 is a zero of the polynomial p(x) = x² - 4.
11.Find the zeroes of the polynomial 2x² - 8.
12.At most how many zeroes can a quadratic polynomial have?
13.Write the quadratic polynomial whose zeroes are 5 and -5.
14.Find the sum of the zeroes of the polynomial x² - 3x.
Section C: Numericals & Word Problems (3 Marks Each)
Apply the concepts to solve the problems. Show all working.
15.The sum of two numbers is 7 and their product is 12. Form a quadratic polynomial whose zeroes are these two numbers, and find the numbers.
16.The area of a rectangular field is (x² + 7x + 12) m² and its breadth is (x + 3) m. Find its length in terms of x.
17.Find a quadratic polynomial whose sum of zeroes is -2 and product of zeroes is -15. Hence find its zeroes.
18.If 2 is one zero of the polynomial p(x) = x² - 6x + k, find the value of k and the other zero.
19.Two zeroes of a polynomial are -2 and 3. Write the quadratic polynomial and find its value at x = 0.
20.A teacher distributed (x³ - x) pencils equally among x students. If the pencils were fully distributed, how many pencils did each student get?
Answer Key
1. b) 2
2. a) 3 and -3
3. a) 5
4. a) -3 and -4
5. d) 3
6. a) 2 and 1
7. Refer to solution guide.
8. Refer to solution guide.
9. Refer to solution guide.
10. Refer to solution guide.
11. Refer to solution guide.
12. Refer to solution guide.
13. Refer to solution guide.
14. Refer to solution guide.
15. Refer to solution guide.
16. Refer to solution guide.
17. Refer to solution guide.
18. Refer to solution guide.
19. Refer to solution guide.
20. Refer to solution guide.
End of Worksheet
People Also Ask
What is the degree of a quadratic polynomial?
2, option (b) in this worksheet (Q1).
What are the zeroes of x² − 9?
3 and −3, option (a) in this worksheet (Q2).
What are the zeroes of x² + 7x + 12?
−3 and −4, option (a) in this worksheet (Q4).
Stuck on a similar problem? Clear your next doubt instantly with the Doubt Solver.
Browse more free worksheets for CBSE Grade 10.