Quantitative Aptitude: Quadratic Equations Set 19

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. 3x2 + 8x + 4 = 0,
    II. 2y2 – 7y – 4 = 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 + 8x + 4 = 0
    3x2 + 6x + 2x + 4 = 0
    Gives x = -2/3, -2
    2y2 – 7y – 4 = 0
    2y2 + y – 8y – 4 = 0
    Gives y = 4, -1/2
    Put all values on number line and analyze the relationship
    -2…. -2/3….-1/2….. 4
  2. I. 2x2 – 13x + 20 = 0,
    II. 3y2 + 4y – 20 = 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 A
    Solution: 

    2x2 – 13x + 20 = 0
    2x2 – 8x – 5x + 20 = 0
    Gives x = 5/2, 4
    3y2 + 4y – 20 = 0
    3y2 – 6y + 10y – 20 = 0
    Gives y = 2, -10/3
  3. I. 3x2 + x – 14 = 0,
    II. 3y2 – 5y – 12 = 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 + x – 14 = 0
    3x2 – 6x + 7x – 14 = 0
    Gives x = 2, -7/3
    3y2 – 5y – 12 = 0
    3y2 – 9y + 4y – 12 = 0
    Gives y = -4/3, 3
  4. I. 3x2 – 2x – 21 = 0,
    II. 3y2 + 19y + 28 = 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: 

    3x2 – 2x – 21 = 0
    3x2 – 9x + 7x – 21 = 0
    Gives x = -7/3, 3
    3y2 + 19y + 28 = 0
    3y2 + 12y + 7y + 28 = 0
    Gives y= -7/3, -4
  5. I. 4x2 + 23x + 28 = 0,
    II. 4y2 – y – 14 = 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: 

    4x2 + 23x + 28 = 0
    4x2 + 16x + 7x + 28 = 0
    Gives x = -4, -7/4
    4y2 – y – 14 = 0
    4y2 – 8y + 7y – 14 = 0
    Gives y= -7/4, 2
  6. I. 4x2 + x – 18 = 0,
    II. 4y2 – 3y – 27 = 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: 

    4x2 + x – 18 = 0
    4x2 – 8x + 9x – 18 = 0
    Gives x = -9/4, 2
    4y2 – 3y – 27 = 0
    4y2 – 12y + 9y – 27 = 0
    Gives y = -9/4, 3
  7. I. 3x2 – 16x + 21 = 0,
    II. 2y2 – y – 6 = 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 – 16x + 21 = 0
    3x2 – 9x – 7x + 21 = 0
    Gives x = 3, 7/3
    2y2 – y – 6 = 0
    2y2 – 4y + 3y – 6 = 0
    So y = -3/2, 2
  8. I. 3x2 + x – 2 = 0,
    II. 4y2 + 13y + 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 A
    Solution: 

    3x2 + x – 2 = 0
    3x2 + 3x – 2x – 2 = 0
    Gives x = -1/3, 2
    4y2 + 13y + 10 = 0
    4y2 + 8y + 5y + 10 = 0
    So y = -2, -5/4
  9. I. 4x2 + 29x + 45 = 0,
    II. 4y2 – 3y – 27 = 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: 

    4x2 + 29x + 45 = 0
    4x2 + 20x + 9x + 45 = 0
    Gives x = -5, -9/4
    4y2 – 3y – 27 = 0
    4y2 – 12y + 9y – 27 = 0
    So y = -9/4, 3
  10. I. 3x2 – 22x + 35 = 0,
    II. 3y2 – 16y + 21 = 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: 

    3x2 – 22x + 35 = 0
    3x2 – 15x – 7x + 35 = 0
    Gives x = 7/3, 5
    3y2 – 16y + 21 = 0
    3y2 – 9y – 7y + 21 = 0
    So y = 7/3, 3

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