BANK & INSURANCE (QUADRATIC EQUATION PART 3)

Total Questions: 50

11. I. 2x² - 7x + 6 = 0  

II. 20y² - 29y + 6 = 0

Correct Answer: (a) x > y
Solution:

From I:
2x² - 7x + 6 = 0
2x² - 4x - 3x + 6 = 0
2x(x - 2) - 3(x - 2) = 0
(2x - 3)(x - 2) = 0
x = 3/2, 2 = 1.5, 2

From II:
20y² - 29y + 6 = 0
20y² - 24y - 5y + 6 = 0
4y(5y - 6) - 1(5y - 6) = 0
(4y - 1)(5y - 6) = 0
y = 1/4, 6/5 = 0.25, 1.2

12. I. x² + 27x + 180 = 0 

II. y² + 31y + 240 = 0

Correct Answer: (d) x ≥ y
Solution:

From I:
x² + 27x + 180 = 0
x² + 15x + 12x + 180 = 0
x(x + 15) + 12(x + 15) = 0
(x + 15)(x + 12) = 0
x = -15, -12

From II:

y² + 31y + 240 = 0
y² + 16y + 15y + 240 = 0
y(y + 16) + 15(y + 16) = 0
(y + 16)(y + 15) = 0
y = -16, -15

13. I. x² = 196      

II. y² + 15y = 0

Correct Answer: (c) x = y or No relation
Solution:From I:
x² = 196
x = -14, 14

From II:
y² + 15y = 0
y(y + 15) = 0
y = 0, -15

14. I. 5x² - 9x + 4 = 0  

II. 20y² - 27y + 9 = 0

Correct Answer: (a) x > y
Solution:

 From I:
5x² - 9x + 4 = 0
5x² - 5x - 4x + 4 = 0
5x(x - 1) - 4(x - 1) = 0
(5x - 4)(x - 1) = 0
x = 4/5, 1

From II:
20y² - 27y + 9 = 0
20y² - 15y - 12y + 9 = 0
5y(4y - 3) - 3(4y - 3) = 0
(5y - 3)(4y - 3) = 0
y = 3/5, 3/4

15. I. x² - 23x + 126 = 0 

II. y² - 22y + 105 = 0

Correct Answer: (c) x = y or No relation
Solution:

 From I:
x² - 23x + 126 = 0
x² - 9x - 14x + 126 = 0
x(x - 9) - 14(x - 9) = 0
(x - 9)(x - 14) = 0
x = 9, 14

From II:
y² - 22y + 105 = 0
y² - 7y - 15y + 105 = 0
y(y - 7) - 15(y - 7) = 0
(y - 7)(y - 15) = 0
y = 7, 15

16. I. x² + 180 = 20 + 26x 

II. y² - 25y + 126 = 0

Correct Answer: (c) x = y or No relation
Solution:

From I:
x² + 180 = 20 + 26x
x² - 26x + 160 = 0
x² - 16x - 10x + 160 = 0
x(x - 16) - 10(x - 16) = 0
(x - 10)(x - 16) = 0
x = 10, 16

From II:
y² - 25y + 126 = 0
y² - 18y - 7y + 126 = 0
y(y - 18) - 7(y - 18) = 0
(y - 7)(y - 18) = 0
y = 7, 18

17. I. x² - 9x - 90 = 0 

II. y² - 35y + 300 = 0

Correct Answer: (e) x ≤ y
Solution:

 From I:
x² - 9x - 90 = 0
x² - 15x + 6x - 90 = 0
x(x - 15) + 6(x - 15) = 0
(x + 6)(x - 15) = 0
x = -6, 15

From II:
y² - 35y + 300 = 0
y² - 20y - 15y + 300 = 0
y(y - 20) - 15(y - 20) = 0
(y - 15)(y - 20) = 0
y = 15, 20

18. I. 4x² + 155 = 2091  

II. 8y² + 472 = 2y² + 2206

Correct Answer: (c) x = y or No relation
Solution:

From I:
4x² + 155 = 2091
4x² = 1936
x² = 484
x = ±22

From II:
8y² + 472 = 2y² + 2206
6y² = 1734
y² = 289
y = ±17

19. I. x² - 37x + 322 = 0 

II. 4y³ - (11)² = y³ + 1415

Correct Answer: (a) x > y
Solution:

From I:
x² - 37x + 322 = 0
x² - 23x - 14x + 322 = 0
x(x - 23) - 14(x - 23) = 0
(x - 14)(x - 23) = 0
x = 14, 23

From II:
4y³ - (11)² = y³ + 1415
3y³ = 1415 + 121
y³ = 512
y = 8

20. I. x² + 27x + 170 = 0 

II. y² + 17y + 70 = 0

Correct Answer: (e) x ≤ y
Solution:

From I:
x² + 27x + 170 = 0
x² + 17x + 10x + 170 = 0
x(x + 17) + 10(x + 17) = 0
(x + 10)(x + 17) = 0
x = -10, -17

From II:
y² + 17y + 70 = 0
y² + 10y + 7y + 70 = 0
y(y + 10) + 7(y + 10) = 0
(y + 7)(y + 10) = 0
y = -7, -10