BANK & INSURANCE (QUADRATIC EQUATION PART 2)

Total Questions: 50

31. I. x² - 20x + 96 = 0 

II. y² - 23y + 132 = 0

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

From I:
x² - 20x + 96 = 0
x² - 12x - 8x + 96 = 0
x(x - 12) - 8(x - 12) = 0
(x - 12)(x - 8) = 0
x = 12, 8

From II:
y² - 23y + 132 = 0
y² - 12y - 11y + 132 = 0
y(y - 12) - 11(y - 12) = 0
(y - 12)(y - 11) = 0
y = 12, 11

32. I. 5x² + 2x - 24 = 0 

II. y² + 3y - 54 = 0

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

From I:
5x² + 2x - 24 = 0
5x² - 10x + 12x - 24 = 0
5x(x - 2) + 12(x - 2) = 0
(5x + 12)(x - 2) = 0
x = -12/5, 2
x = -2.4, 2

From II:
y² + 3y - 54 = 0
y² - 6y + 9y - 54 = 0
y(y - 6) + 9(y - 6) = 0
(y + 9)(y - 6) = 0
y = -9, 6

33. I. x² + 23x + 112 = 0 

II. 4y² + 24y + 35 = 0

Correct Answer: (b) x ≤ y
Solution:

From I:
x² + 23x + 112 = 0
x² + 16x + 7x + 112 = 0
x(x + 16) + 7(x + 16) = 0
(x + 16)(x + 7) = 0
x = -16, -7

From II:
4y² + 24y + 35 = 0
4y² + 10y + 14y + 35 = 0
2y(2y + 5) + 7(2y + 5) = 0
(2y + 5)(2y + 7) = 0
y = -5/2, -7/2
y = -2.5, -3.5

34. I. x + 10√x + 24 = 0 

II. y + 7√y + 12 = 0

Correct Answer: (d) x > y
Solution:

From I:
x + 10√x + 24 = 0
x + 4√x + 6√x + 24 = 0
√x(√x + 4) + 6(√x + 4) = 0
(√x + 4)(√x + 6) = 0
√x = -4, -6
x = 16, 36

From II:
y + 7√y + 12 = 0
y + 3√y + 4√y + 12 = 0
√y(√y + 3) + 4(√y + 3) = 0
(√y + 3)(√y + 4) = 0
√y = -3, -4
y = 9, 16

35. I. x² - 24x + 135 = 0 

II. y² - 32y + 256 = 0

Correct Answer: (b) x ≤ y
Solution:

From I:
x² - 24x + 135 = 0
x² - 15x - 9x + 135 = 0
x(x - 15) - 9(x - 15) = 0
(x - 15)(x - 9) = 0
x = 15, 9

From II:
y² - 32y + 256 = 0
y² - 16y - 16y + 256 = 0
y(y - 16) - 16(y - 16) = 0
(y - 16)(y - 16) = 0
y = 16

36. I. (x + 4)² = -(4x + 16) 

II. (y - 4)² = 36 - 7y

Correct Answer: (e) x ≥ y
Solution:

From I:
(x + 4)² = -(4x + 16)
x² + 8x + 16 = -(4x + 16)
x² + 12x + 32 = 0
x² + 4x + 8x + 32 = 0
x(x + 4) + 8(x + 4) = 0
(x + 4)(x + 8) = 0
x = -4, -8

From II:
(y - 4)² = 36 - 7y
y² - 8y + 16 = 36 - 7y
y² - y - 20 = 0
y² - 5y + 4y - 20 = 0
y(y - 5) + 4(y - 5) = 0
(y - 5)(y + 4) = 0
y = -4, 5

37. I. x³ = -343     

II. y² + 17y + 72 = 0

Correct Answer: (a) x < y
Solution:

From I:
x³ = -343
x = -7

From II:
y² + 17y + 72 = 0
y² + 8y + 9y + 72 = 0
y(y + 8) + 9(y + 8) = 0
(y + 8)(y + 9) = 0
y = -8, -9

38. I. x² + 2.1x + 0.9 = 0 

II. y² + 0.3y - 0.1 = 0

Correct Answer: (b) x ≤ y
Solution:

From I:
x² + 2.1x + 0.9 = 0
x² + 0.6x + 1.5x + 0.9 = 0
x(x + 0.6) + 1.5(x + 0.6) = 0
(x + 0.6)(x + 1.5) = 0
x = -0.6, -1.5

From II:
y² + 0.3y - 0.1 = 0
y² + 0.5y - 0.2y - 0.1 = 0
y(y + 0.5) - 0.2(y + 0.5) = 0
(y + 0.5)(y - 0.2) = 0
y = -0.5, 0.2

39. I. x² = 64      

II. y² + 16y + 63 = 0

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

From I:
x² = 64
x = -8, 8

From II:
y² + 16y + 63 = 0
y² + 7y + 9y + 63 = 0
y(y + 7) + 9(y + 7) = 0
(y + 7)(y + 9) = 0
y = -7, -9

40. I. x² + x - 20 = 0  

II. y² + 17y + 72 = 0

Correct Answer: (a) x < y
Solution:

From I:
x² + x - 20 = 0
x² + 5x - 4x - 20 = 0
x(x + 5) - 4(x + 5) = 0
(x + 5)(x - 4) = 0
x = -5, 4

From II:

y² + 17y + 72 = 0
y² + 8y + 9y + 72 = 0
y(y + 8) + 9(y + 8) = 0
(y + 8)(y + 9) = 0
y = -8, -9