Quantitative Aptitude: Quadratic Equations Set 20

Quadratic Equations Practice Sets IBPS PO NICL, NIACL, LIC, Dena Bank PO PGDBF, BOI, Bank of Baroda and other competitive exams

Directions: In the following questions, two equations numbered are given in variables x and y. You have to solve both the equations and find out the relationship between x and y. Then give answer accordingly-

  1. I. 4x2 – 9x – 9 = 0,
    II. 4y2 + 11y + 6 = 0
    A) If x > y
    B) If x < y
    C) If x ≥ y
    D) If x ≤ y
    E) If x = y or relation cannot be established
    View Answer
     Option C
    Solution: 

    4x2 – 9x – 9 = 0
    4x2 – 12x + 3x – 9 = 0
    Gives x = -3/4, 3
    4y2 + 11y + 6 = 0
    4y2 + 8y + 3y + 6 = 0
    Gives y = -2, -3/4
    Put all values on number line and analyze the relationship
    -2…. -3/4….3
  2. I. 3x2 – 2x – 21 = 0,
    II. 6y2 + 17y + 7 = 0
    A) If x > y
    B) If x < y
    C) If x ≥ y
    D) If x ≤ y
    E) If x = y or relation cannot be established
    View Answer
     Option E
    Solution: 

    3x2 – 2x – 21 = 0
    3x2 – 9x + 7x – 21 = 0
    Gives x = -7/3, 3
    6y2 + 17y + 7 = 0
    6y2 + 3y + 14y + 7 = 0
    Gives y = -7/3, -1/2
  3. I. 3x2 – 13x + 14 = 0,
    II. 3y2 – 20y + 32 = 0
    A) If x > y
    B) If x < y
    C) If x ≥ y
    D) If x ≤ y
    E) If x = y or relation cannot be established
    View Answer
     Option B
    Solution: 

    3x2 – 13x + 14 = 0
    3x2 – 6x – 7x + 14 = 0
    Gives x = 2, 7/3
    3y2 – 20y + 32 = 0
    3y2 – 12y – 8y + 32 = 0
    Gives y = 8/3, 4
  4. I. 3x2 – 2x – 16 = 0,
    II. 3y2 – 20y + 32 = 0
    A) If x > y
    B) If x < y
    C) If x ≥ y
    D) If x ≤ y
    E) If x = y or relation cannot be established
    View Answer
     Option D
    Solution: 

    3x2 – 2x – 16 = 0
    3x2 – + 6x – 8x – 16 = 0
    Gives x = -2, 8/3
    3y2 – 20y + 32 = 0
    3y2 – 12y – 8y + 32 = 0
    Gives y = 8/3, 4
  5. I. 5x2 – 16x – 16 = 0,
    II. 3y2 – 14y + 8 = 0
    A) If x > y
    B) If x < y
    C) If x ≥ y
    D) If x ≤ y
    E) If x = y or relation cannot be established
    View Answer
     Option E
    Solution: 

    5x2 – 16x – 16 = 0
    5x2 – 20x + 4x – 16 = 0
    Gives x = -4/5, 4
    3y2 – 14y + 8 = 0
    3y2 – 12y – 2y + 8 = 0
    Gives y= 2/3, 4
  6. I. 4x2 – 17x + 18 = 0,
    II. 3y2 – 2y – 8 = 0
    A) If x > y
    B) If x < y
    C) If x ≥ y
    D) If x ≤ y
    E) If x = y or relation cannot be established
    View Answer
     Option C
    Solution: 

    4x2 – 17x + 18 = 0
    4x2 – 8x – 9x + 18 = 0
    Gives x = 2, 9/4
    3y2 – 2y – 8 = 0
    3y2 – 6y + 4y – 8 = 0
    Gives y = -4/3, 2
  7. I. 2x2 – 5x – 12 = 0,
    II. 3y2 – 17y + 10 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relationship cannot be determined
    View Answer
     Option E
    Solution: 

    2x2 – 5x – 12 = 0
    2x2 – 8x + 3x – 12 = 0
    Gives x = -3/2, 4
    3y2 – 17y + 10 = 0
    3y2 – 15y – 2y + 10 = 0
    So y = 2/3, 5
  8. I. 3x2 + 2x – 16 = 0,
    II. y2 + 11y + 24 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relationship cannot be determined
    View Answer
     Option A
    Solution: 

    3x2 + 2x – 16 = 0
    3x2 – 6x + 8x – 16 = 0
    Gives x = -8/3, 2
    y2 + 11y + 24 = 0
    y2 + 8y + 3y + 24 = 0
    So y = -8, -3
  9. I. 3x2 + 10x + 8 = 0,
    II. 3y2 – 11y – 20 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relationship cannot be determined
    View Answer
     Option D
    Solution: 

    3x2 + 10x + 8 = 0
    3x2 + 6x + 4x + 8 = 0
    Gives x = -2, -4/3
    3y2 – 11y – 20 = 0
    3y2 – 15y + 4y – 20 = 0
    So y = -4/3, 5
  10. I. 4x2 + 23x + 15 = 0,
    II. 3y2 – 19y – 14 = 0
    A) x > y
    B) x < y
    C) x ≥ y
    D) x ≤ y
    E) x = y or relationship cannot be determined
    View Answer
     Option B
    Solution: 

    4x2 + 23x + 15 = 0
    4x2 + 20x + 3x + 15 = 0
    Gives x = -5, -3/4
    3y2 – 19y – 14 = 0
    3y2 – 21y + 2y – 14 = 0
    So y = -2/3, 7

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