BANK & INSURANCE (QUADRATIC EQUATION PART 1)

Total Questions: 50

41. I. x² + 16x + 60 = 0 

II. y² + 18y - 144 = 0

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

From I:
x² + 16x + 60 = 0
x² + 10x + 6x + 60 = 0
x(x + 10) + 6(x + 10) = 0
(x + 10)(x + 6) = 0
x = -6, -10

From II:
y² + 18y - 144 = 0
y² + 24y - 6y - 144 = 0
y(y + 24) - 6(y + 24) = 0
(y + 24)(y - 6) = 0
y = 6, -24

42. I. x² - 32x - 185 = 0 

II. y² + 28y - 165 = 0

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

From I:
x² - 32x - 185 = 0
x² - 37x + 5x - 185 = 0
x(x - 37) + 5(x - 37) = 0
(x - 37)(x + 5) = 0
x = 37, -5

From II:
y² + 28y - 165 = 0
y² + 33y - 5y - 165 = 0
y(y + 33) - 5(y + 33) = 0
(y + 33)(y - 5) = 0
y = 5, -33

43. I. 4x² + 10x + 6 = 0  

II. 7y² + 11y - 18 = 0

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

From I:
4x² + 10x + 6 = 0
4x² + 4x + 6x + 6 = 0
4x(x + 1) + 6(x + 1) = 0
(x + 1)(4x + 6) = 0
x = -1, -3/2

From II:
7y² + 11y - 18 = 0
7y² + 18y - 7y - 18 = 0
7y(y - 1) + 18(y - 1) = 0
(y - 1)(7y + 18) = 0
y = 1, -18/7

44. I. x² - 2401 = 0   

II. y = √2401

Correct Answer: (e) x ≥ y
Solution:

44. (e): From I:
x² - 2401 = 0
x² = 2401
x = ±49

From II:
y = √2401
y = 49

45. I. x² + 48x + 576 = 0 

II. y² + 56y - 784 = 0

Correct Answer: (a) x < y
Solution:

From I:
x² + 48x + 576 = 0
x² + 24x + 24x + 576 = 0
x(x + 24) + 24(x + 24) = 0
(x + 24)(x + 24) = 0
x = -24, -24

From II:
y² + 56y + 784 = 0
y² + 28y + 28y + 784 = 0
y(y + 28) + 28(y + 28) = 0
(y + 28)(y + 28) = 0
y = -28, -28

46. I. x² + 24x + 140 = 0 

II. y² + 8y - 128 = 0

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

From I:
x² + 24x + 140 = 0
x² + 14x + 10x + 140 = 0
x(x + 14) + 10(x + 14) = 0
(x + 14)(x + 10) = 0
x = -14, -10

From II:
y² + 8y - 128 = 0
y² + 16y - 8y - 128 = 0
y(y + 16) - 8(y + 16) = 0
(y + 16)(y - 8) = 0
y = 8, -16

47. I. x² + 48x + 576 = 0 

II. y² + 24y + 108 = 0

Correct Answer: (b) x ≤ y
Solution:

From I:
x² + 48x + 576 = 0
x² + 2 × 24 × x + 24² = 0
(x + 24)² = 0
x = -24, -24

From II:
y² + 24y + 108 = 0
y² + 18y + 6y + 108 = 0
y(y + 18) + 6(y + 18) = 0
(y + 6)(y + 18) = 0
y = -6, -18

48. I. x² = 2601      

II. y² = 2401

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

From I:
x² = 2601
x = ±51

From II:
y² = 2401
y = ±49

49. I. 5x² = 30x - 40   

II. 3y² - 7y + 4 = 0

Correct Answer: (a) x < y
Solution:

From I:
5x² = 30x - 40
5x² - 30x + 40 = 0
5x² - 20x - 10x + 40 = 0
5x(x - 4) - 10(x - 4) = 0
(5x - 10)(x - 4) = 0
x = 2, 4

From II:
3y² - 7y + 4 = 0
3y² - 3y - 4y + 4 = 0
3y(y - 1) - 4(y - 1) = 0
(y - 1)(3y - 4) = 0
y = 1, 4/3

50. I. 5x + y = 40    

II. x - y + 4 = 0

Correct Answer: (b) x ≤ y
Solution:

From I:
5x + y = 40
y = 40 - 5x

From II:
x - y + 4 = 0
x - y = -4
x - (40 - 5x) = -4
6x - 40 = -4
6x = 36
x = 6

So, y = 40 - 30 = 10