Quadratic Equations Set – 6

1. 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

Answer & Explanation

 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

 

2. I. 3x2 – 5x – 12 = 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

Answer & Explanation

 Option C
Solution: 

3x2 – 5x – 12 = 0
3x2 – 9x + 4x – 12 = 0
Gives x = -4/3, 3
3y2 + 16y + 16 = 0
3y2 + 12y + 4y + 16 = 0
Gives y = -4, -4/3
Put all values on number line and analyze the relationship
-4….. -4/3….. 3

 

3. I. 4x2 + 17x + 18 = 0
II. 4y2 – 3y – 27 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Answer & Explanation

 Option E
Solution: 

4x2 + 17x + 18 = 0
4x2 + 8x + 9x + 18 = 0
Gives x = -2, -9/4
4y2 – 3y – 27 = 0
4y2 – 12y + 9y – 27 = 0
Gives y = -9/4, 3
Put all values on number line and analyze the relationship
-9/4…… -2…… 3
 

 

4. I. 3x2 – x – 24 = 0
II. 4y2 + 5y – 6 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Answer & Explanation

 Option E
Solution: 

3x2 – x – 24 = 0
3x2 – 9x + 8x – 24 = 0
Gives x = -8/3, 3
4y2 + 5y – 6 = 0
4y2 + 8y – 3y – 6 = 0
Gives y = -2, 3/4
Put all values on number line and analyze the relationship
-8/3…… -2….. 3/4…… 3

 

5. I. 4x2 – 9x – 9 = 0
II. 2y2 + 17y + 35 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Answer & Explanation

 Option A
Solution: 

4x2 – 9x – 9 = 0
4x2 – 12x + 3x – 9 = 0
Gives x = 3, -3/4
2y2 + 17y + 35 = 0
2y2 + 10y + 7y + 35 = 0
Gives y = -7/2, -5
Put all values on number line and analyze the relationship
-5……. -7/2…… -3/4….. 3

 

6. I. 3x2 + 2x – 21 = 0
II. 6y2 – 5y – 21 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Answer & Explanation

 Option E
Solution: 

3x2 + 2x – 21 = 0
3x2 + 9x – 7x – 21 = 0
Gives x = -3, 7/3
6y2 – 5y – 21 = 0
6y2 + 9y – 14y – 21 = 0
Gives y = -3/2, 7/3
Put all values on number line and analyze the relationship
-3….. -3/2….. 7/3

 

7. I. 15x2 – 29x + 12 = 0
II. 15y2 – 22y + 8 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Answer & Explanation

 Option E
Solution: 

15x2 – 29x + 12 = 0
15x2 – 9x – 20x + 12 = 0
Gives x = 3/5, 4/3
15y2 – 22y + 8 = 0
15y2 – 10y – 12y + 8 = 0
Gives y = 4/5, 2/3
Put all values on number line and analyze the relationship
3/5….. 2/3….. 4/5…. 4/3

 

8. I. 4x2 + 9x – 9 = 0
II. 4y2 – 19y + 12 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Answer & Explanation

 Option D
Solution: 

4x2 + 9x – 9 = 0
4x2 + 12x – 3x – 9 = 0
Gives x = -3, 3/4
4y2 – 19y + 12 = 0
4y2 – 16y – 3y + 12 = 0
Gives y = 3/4, 4
Put all values on number line and analyze the relationship
-3…….. 3/4….. 4

 

9. I. 3x2 + 19x + 28 = 0
II. 3y2 + 13y + 14 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Answer & Explanation

 Option D
Solution: 

3x2 + 19x + 28 = 0
3x2 + 12x + 7x + 28 = 0
Gives x = -4, -7/3
3y2 + 13y + 14 = 0
3y2 + 6y + 7y + 14 = 0
Gives y = -7/3, -2
Put all values on number line and analyze the relationship
-4…… -7/3…… -2

 

10. I. 2x2 – 19x + 42 = 0
II. 3y2 – 13y + 12 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relation cannot be established

Answer & Explanation

 Option A
Solution: 

2x2 – 19x + 42 = 0
2x2 – 12x – 7x + 42 = 0
Gives x = 7/2, 6
3y2 – 13y + 12 = 0
3y2 – 9y + 4y + 12 = 0
Gives y = 4/3, 3
Put all values on number line and analyze the relationship
4/3…… 3…… 7/2….. 6

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