1. Find the roots of the quadratic equation: x2 + 2x – 15 = 0?
A. -5, 3
B. 3, 5
C. -3, 5
D. -3, -5
E. 5, 2
2. Find the roots of the quadratic equation: 2×2 + 3x – 9 = 0?
A. 3, -3/2
B. 3/2, -3
C. -3/2, -3
D. 3/2, 3
E. 2/3, -3
3. The roots of the equation 3×2 – 12x + 10 = 0 are?
A. rational and unequal
B. complex
C. real and equal
D. irrational and unequal
E. rational and equal
4. If the roots of a quadratic equation are 20 and -7, then find the equation?
A. x2 + 13x – 140 = 0
B. x2 – 13x + 140 = 0
C. x2 – 13x – 140 = 0
D. x2 + 13x + 140 = 0
E. None of these
5. The sum and the product of the roots of the quadratic equation x2 + 20x + 3 = 0 are?
A. 10, 3
B. -10, 3
C. 20, -3
D. -10, -3
E. None of these
6. If the roots of the equation 2×2 – 5x + b = 0 are in the ratio of 2:3, then find the value of b?
A. 3
B. 4
C. 5
D. 6
E. None of these
7. The sum of the squares of two consecutive positive integers exceeds their product by 91. Find the integers?
A. 9, 10
B. 10, 11
C. 11, 12
D. 12, 13
E. None of these
8. One root of the quadratic equation x2 – 12x + a = 0, is thrice the other. Find the value of a?
A. 29
B. -27
C. 28
D. 7
E. None of these
9. The sum of the square of the three consecutive even natural numbers is 1460. Find the numbers?
A. 18, 20, 22
B. 20, 22, 24
C. 22, 24, 26
D. 24, 26, 28
E. None of these
10. If a and b are the roots of the equation x2 – 9x + 20 = 0, find the value of a2 + b2 + ab?
A. -21
B. 1
C. 61
D. 21
E. None of these
11. Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 8x + 4 = 0?
A. 15
B. 14
C. 24
D. 26
E. None of these
12. Find the quadratic equations whose roots are the reciprocals of the roots of 2×2 + 5x + 3 = 0?
A. 3×2 + 5x – 2 = 0
B. 3×2 + 5x + 2 = 0
C. 3×2 – 5x + 2 = 0
D. 3×2 – 5x – 2 = 0
E. None of these
13. A man could buy a certain number of notebooks for Rs.300. If each notebook cost is Rs.5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook?
A. 10
B. 8
C. 15
D. 7.50
E. None of these
14. I. a2 – 7a + 12 = 0,
II. b2 – 3b + 2 = 0 to solve both the equations to find the values of a and b?
A. if a < b B. if a ≤ b C. if the relationship between a and b cannot be established. D. if a > b E. if a ≥ b
15. I. x2 + 9x + 20 = 0,
II. y2 + 5y + 6 = 0 to solve both the equations to find the values of x and y?
A. If x < y B. If x > y
C. If x ≤ y
D. If x ≥ y
E. If x = y or the relationship between x and y cannot be established.
16. I. a2 – 9a + 20 = 0,
II. 2b2 – 5b – 12 = 0 to solve both the equations to find the values of a and b?
A. If a < b B. If a ≤ b C. If the relationship between a and b cannot be established D. If a > b
E. If a ≥ b
17. I. a2 + 11a + 30 = 0,
II. b2 + 6b + 5 = 0 to solve both the equations to find the values of a and b?
A. If a < b B. If a ≤ b C. If the relationship between a and b cannot be established D. If a > b
E. If a ≥ b
18. I. a2 + 8a + 16 = 0,
II. b2 – 4b + 3 = 0 to solve both the equations to find the values of a and b?
A. If a < b B. If a ≤ b C. If the relationship between a and b cannot be established D. If a > b
E. If a ≥ b
19. I. a2 – 2a – 8 = 0,
II. b2 = 9 to solve both the equations to find the values of a and b?
A. If a < b B. If a ≤ b C. If the relationship between a and b cannot be established D. If a > b
E. If a ≥ b
20. I. x2 + 5x + 6 = 0,
II. y2 + 9y +14 = 0 to solve both the equations to find the values of x and y?
A. If x < y B. If x > y
C. If x ≤ y
D. If x ≥ y
E. If x = y or the relationship between x and y cannot be established.
ANSWERS
1. A
2. B
3. D
4. C
5. E
6. A
7. A
8. E
9. B
10. C
11. B
12. B
13. A
14. D
15. A
16. E
17. B
18. A
19. C
20. E
