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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