Quadratic Equations Set – 21

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

Answer & Explanation

 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

Answer & Explanation

 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

Answer & Explanation

 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

Answer & Explanation

 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

Answer & Explanation

 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

Answer & Explanation

  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

Answer & Explanation

 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

Answer & Explanation

 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

Answer & Explanation

 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

Answer & Explanation

 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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