Number Series, Quadratic Equations - Question Bank

1. Find the missing term in the series: 1, 0, -1, -2, ...
A) -3
B) -4
C) -5
D) -6
2. If one root of the quadratic equation x^2 - ax + 12 = 0 is 3, what is the value of 'a'?
A) 4
B) 5
C) 6
D) 7
3. What is the next number in the series: 8, 12, 18, 27, ...?
A) 36
B) 38.5
C) 40.5
D) 42
4. Consider the quadratic equation 2x^2 - 5x + 2 = 0. What are the roots?
A) 2 and 1/2
B) -2 and -1/2
C) 2 and -1/2
D) -2 and 1/2
5. Find the missing term in the series: 1, 1, 4, 8, 16, ...
A) 20
B) 24
C) 32
D) 64
6. If the product of the roots of the quadratic equation 3x^2 - 15x + c = 0 is 5, what is the value of c?
A) 5
B) 10
C) 15
D) 20
7. What is the next number in the series: 10, 12, 16, 22, 30, ...?
A) 38
B) 40
C) 42
D) 44
8. For the quadratic equation x^2 - 4 = 0, the roots are:
A) 2
B) -2
C) 2 and -2
D) 4
9. Find the missing term in the series: 2, 3, 5, 7, 11, __
A) 13
B) 15
C) 17
D) 19
10. If one root of the quadratic equation x^2 + kx - 10 = 0 is 2, what is the value of k?
A) -3
B) 3
C) -5
D) 5
11. What is the next number in the series: 5, 25, 125, 625, ...?
A) 1125
B) 3125
C) 15625
D) 78125
12. Consider the quadratic equation x^2 + 6x + 9 = 0. What are the roots?
A) 3 and 3
B) -3 and -3
C) 3 and -3
D) 9
13. Find the missing term: 0, 1, 3, 7, 15, ...
A) 20
B) 23
C) 31
D) 35
14. If the sum of the roots of the quadratic equation 2x^2 + bx + 8 = 0 is 4, what is the value of b?
A) -8
B) 8
C) -4
D) 4
15. What is the next number in the series: 6, 12, 20, 30, 42, ...?
A) 50
B) 54
C) 56
D) 60
16. Consider the quadratic equation 4x^2 - 7x + 3 = 0. What are the roots?
A) 1 and 3/4
B) -1 and -3/4
C) 1 and -3/4
D) -1 and 3/4
17. Find the missing term in the series: 1, 2, 4, 8, __, 32
A) 12
B) 16
C) 20
D) 24
18. For the quadratic equation 9x^2 - 6x + 1 = 0, the roots are:
A) Real and distinct
B) Real and equal
C) Imaginary
D) Zero
19. What is the next number in the series: 15, 18, 21, 24, ...?
A) 25
B) 26
C) 27
D) 28
20. If one root of the quadratic equation x^2 - 5x + c = 0 is 2, what is the other root?
A) 1
B) 3
C) 4
D) 5
21. Find the missing term in the series: 3, 4, 7, 11, 18, ...
A) 25
B) 29
C) 30
D) 32
22. Consider the quadratic equation 5x^2 + 2x + 1 = 0. What is the nature of the roots?
A) Real and distinct
B) Real and equal
C) Imaginary
D) One positive, one negative
23. What is the next number in the series: 1, 8, 27, 64, ...?
A) 100
B) 125
C) 150
D) 216
24. If the roots of the quadratic equation x^2 - 10x + k = 0 are real and equal, what is the value of k?
A) 20
B) 25
C) 30
D) 35
25. Find the missing number: 10, 15, 25, 40, 65, ...
A) 90
B) 100
C) 105
D) 110
26. Consider the quadratic equation 3x^2 - 2x - 1 = 0. What are the roots?
A) 1 and -1/3
B) -1 and 1/3
C) 1 and 1/3
D) -1 and -1/3
27. What is the next term in the series: 4, 16, 36, 64, ...?
A) 81
B) 100
C) 121
D) 144
28. If the sum of the roots of the quadratic equation ax^2 + bx + c = 0 is 5 and the product of the roots is 6, what is the equation?
A) x^2 + 5x + 6 = 0
B) x^2 - 5x + 6 = 0
C) x^2 + 6x + 5 = 0
D) x^2 - 6x + 5 = 0
29. Find the next number in the series: 1, 5, 14, 30, 55, ...
A) 80
B) 85
C) 91
D) 100
30. Consider the quadratic equation 2x^2 + 5x - 3 = 0. What are the roots?
A) 1/2 and -3
B) -1/2 and 3
C) 1/2 and 3
D) -1/2 and -3
31. What is the missing term in the series: 7, 14, 21, 28, __, 42?
A) 30
B) 32
C) 35
D) 36
32. For the quadratic equation 4x^2 - 12x + 9 = 0, the roots are:
A) Real and distinct
B) Real and equal
C) Imaginary
D) Zero
33. Find the next number in the series: 1, 3, 6, 10, 15, ...
A) 18
B) 20
C) 21
D) 24
34. If one root of the quadratic equation x^2 - 7x + k = 0 is 3, what is the value of k?
A) 10
B) 12
C) 15
D) 18
35. What is the next term in the series: 100, 90, 80, 70, ...?
A) 60
B) 65
C) 50
D) 75
36. Consider the quadratic equation y^2 - 9 = 0. What are the values of y?
A) 3
B) -3
C) 3 and -3
D) 9
37. Find the missing term: 2, 6, 12, 20, __, 42
A) 28
B) 30
C) 32
D) 36
38. In the quadratic equation ax^2 + bx + c = 0, if b^2 - 4ac < 0, the roots are:
A) Real and distinct
B) Real and equal
C) Imaginary
D) One positive, one negative
39. What is the next number in the series: 10, 20, 30, 40, ...?
A) 45
B) 50
C) 60
D) 70
40. Solve for x: 3x^2 - 12x + 9 = 0
A) 1 and 3
B) -1 and -3
C) 1 and -3
D) -1 and 3
41. Identify the pattern and find the next term: 5, 10, 20, 40, ...
A) 50
B) 60
C) 80
D) 100
42. Consider the quadratic equation x^2 + x + 1 = 0. What is the nature of its roots?
A) Real and distinct
B) Real and equal
C) Imaginary
D) One root is zero
43. What is the next number in the series: 1, 1, 2, 3, 5, 8, ...?
A) 11
B) 13
C) 16
D) 21
44. If the discriminant (b^2 - 4ac) of a quadratic equation is zero, the roots are:
A) Real and distinct
B) Real and equal
C) Imaginary
D) One positive and one negative
45. Find the missing term in the series: 1, 4, 9, 16, __, 36
A) 20
B) 25
C) 30
D) 32
46. For the quadratic equation 2x^2 + 4x + 2 = 0, what is the nature of the roots?
A) Real and distinct
B) Real and equal
C) Imaginary
D) One real and one imaginary root
47. What is the next number in the series: 3, 7, 15, 31, 63, ...?
A) 94
B) 127
C) 128
D) 150
48. Consider the quadratic equation x^2 - 5x + 6 = 0. What are the roots of this equation?
A) 2 and 3
B) -2 and -3
C) 1 and 6
D) -1 and -6
49. Identify the pattern in the series: 2, 5, 10, 17, 26, ...
A) Add 3, then add 5, then add 7, ...
B) Multiply by 2, then add 1, ...
C) n^2 + 1, where n starts from 1
D) n^2 - 1, where n starts from 2
50. In a quadratic equation ax^2 + bx + c = 0, if the discriminant (b^2 - 4ac) is positive, what can be said about the roots?
A) The roots are real and equal.
B) The roots are real and distinct.
C) The roots are imaginary.
D) There are no real roots.
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