Quantitative Aptitude: Quadratic Equations Set 21

Quadratic Equations Practice Sets for 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 – 4x – 15 = 0,
   II. 3y² + 11y + 10 = 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 – 4x – 15 = 0
   3x² – 9x + 5x – 15 = 0
   Gives x = -5/3, 3
   3y² + 11y + 10 = 0
   3y² + 6y + 5y + 10 = 0
   Gives y = -2. -5/3
   
2. I. 3x² + 17x + 24 = 0,
   II. 3y² – 4y – 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 + 17x + 24 = 0
   3x² + 17x + 24 = 0
   Gives x = -3, -8/3
   3y² – 4y – 32 = 0
   3y² – 12y + 8y – 32 = 0
   Gives y = -8/3, 4
   
3. 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 – 2x – 16 = 0
   Gives x = -2, 8/3
   3y² – 20y + 32 = 0
   3y² – 20y + 32 = 0
   Gives y = 8/3, 4
   
4. I. 2x² + 5x – 12 = 0,
   II. 4y² – 19y – 30 = 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: 
   2x² + 5x – 12 = 0
   2x² + 8x – 3x – 12 = 0
   Gives x = -4, 3/2
   4y² – 19y – 30 = 0
   4y² – 24y +  5y – 30 = 0
   Gives y= -5/4, 6
   
5. I. 2x² – 17x + 36 = 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 A
   Solution: 
   2x² – 17x + 36 = 0
   2x² – 8x – 9x + 36 = 0
   Gives x = 4, 9/2
   3y² – 2y – 8 = 0
   3y² – 6y + 4y – 8 = 0
   Gives y= -4/3, 2
6. I. 3x² + 19x + 30 = 0,
   II. 2y² + 3y – 2 = 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 + 19x + 30 = 0
   3x² + 9x + 10x + 30 = 0
   Gives x = -10/3, -3
   2y² + 3y – 2 = 0
   2y² + 4y – y – 2 = 0
   Gives y = -2, 1/2
   
7. I. 5x² + 11x – 12 = 0,
   II. 3y² + 7y – 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 E
   Solution: 
   5x² + 11x – 12 = 0
   5x² + 15x – 4x – 12 = 0
   Gives x = -3, 4/5
   3y² + 7y – 6 = 0
   3y² + 9y – 2y – 6 = 0
   So y = -3, 2/3
   
8. I. 3x² + x – 10 = 0,
   II. 2y² + 11y + 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 C
   Solution: 
   3x² + x – 10 = 0
   3x² + 6x – 5x – 10 = 0
   Gives x = -2, 5/3
   2y² + 11y + 14 = 0
   2y² + 4y + 7y + 14 = 0
   So y = -7/2, -2
   
9. I. 3x² + 19x + 30 = 0,
   II. 2y² – 3y – 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 B
   Solution: 
   3x² + 19x + 30 = 0
   3x² + 9x + 10x + 30 = 0
   Gives x = -3, -10/3
   2y² – 3y – 20 = 0
   2y² – 8y + 5y – 20 = 0
   So y = -5/2, 4
   
10. I. 2x² – x – 36 = 0,
    II. 2y² – 21y + 54 = 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: 
    2x² – x – 36 = 0
    2x² + 8x – 9x – 36 = 0
    Gives x = -4, 9/2
    2y² – 21y + 54 = 0
    2y² – 12y – 9y + 54 = 0
    So y = 9/2, 6
    

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