# Quadratic Equations Set – 11

1. I. 3x2 – 8x + 4 = 0
II. 3y2 – 16y + 16 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Option E
Solution:

3x2 – 8x + 4 = 0
3x2 – 2x – 6x + 4 = 0
Gives x = 2, 2/3
3y2 – 16y + 16 = 0
3y2 – 12y – 4y + 16 = 0
Gives y = 4, 4/3

2. I. 3x2 + 10x + 7 = 0
II. 2y2 – 5y – 12 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Option E
Solution:

3x2 + 10x + 7 = 0
3x2 + 3x + 7x + 7 = 0
Gives x = -1, -7/3
2y2 – 5y – 12 = 0
2y2 – 8y + 3y – 12 = 0
Gives y = -3/2, 4

3. I. 4x2 + 15x + 9 = 0
II. 4y2 – 13y – 12 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Option D
Solution:

4x2 + 15x + 9 = 0
4x2 + 12x + 3x + 9 = 0
Gives x = -3, -3/4
4y2 – 13y – 12 = 0
4y2 – 16y + 3y – 12 = 0
Gives y = -3/4, 4

4. I. 3x2 + 23x + 30 = 0
II. 3y2 – 4y – 4 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Option B
Solution:

3x2 + 23x + 30 = 0
3x2 + 18x + 5x + 30 = 0
Gives x = -5/3, -6
3y2 – 4y – 4 = 0
3y2 – 6y + 2y – 4 = 0
Gives y = 2, -2/3
Put all values on number line and analyze the relationship
-6…. -5/3….. -2/3…… 2

5. I. 5x2 – 36x – 32 = 0,
II. 3y2 – 11y + 6 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Option E
Solution:

5x2 – 36x – 32 = 0
5x2 + 4x – 40x – 32 = 0
Gives x = -4/5, 8
3y2 – 17y – 6 = 0
3y2 + y – 18y – 6 = 0
Gives y = -1/3, 6

6. I. 4x2 + 17x + 18 = 0,
II. 3y2 + 4y – 4 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Option D

7. I. 4x2 – 9x – 9 = 0,
II. 4y2 + 11y + 6 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Option C

8. I. 3x2 – 19x + 28 = 0,
II. 4y2 – 11y + 6 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Option A

9. I. 3x2 + 19x + 28 = 0,
II. 6y2 – y – 2 = 0A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Option B

10. I. 3x2 + 7x – 6 = 0,
II. 6y2 – y – 2 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established