Quadratic Equations Set – 5

1. I. 3x2 + 22 x + 24 = 0
II. 2y2 + 11y + 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 E
Solution:

3x2 + 22 x + 24 = 0
3x2 + 18x + 4x + 24 = 0
Gives x = -4/3, -6
2y2 + 11y + 12 = 0
2y2 + 8y + 3y + 12 = 0
Gives y = -4, -3/2
Put all values on number line and analyze the relationship
-6…..-4…. -3/2….-4/3

2. I. 20x2 – 31x + 12 = 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 C
Solution:

20x2 – 31x + 12 = 0
20x2 – 16x – 15x + 12 = 0
Gives x = 3/4, 4/5
4y2 + 5y – 6 = 0
4y2 + 5y – 6 = 0
Gives y = -2, 3/4
Put all values on number line and analyze the relationship
-2…. 3/4… 4/5

3. I. 3x2 + 14x – 5 = 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 + 14x – 5 = 0
3x2 + 15x – x – 5 = 0
Gives x = -5, 1/3
4y2 + 5y – 6 = 0
4y2 + 5y – 6 = 0
Gives y = -2, 3/4
Put all values on number line and analyze the relationship
-5….-2….. 1/3…. 3/4

4. I. 2x2 – 15x + 7 = 0
II. 8y2 + 6y – 5 = 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:

2x2 – 15x + 7 = 0
2x2 – 14x – x + 7 = 0
Gives x = 1/2, 7
8y2 + 6y – 5 = 0
8y2 – 4y + 10y – 5 = 0
Gives y = -5/4, 1/2
Put all values on number line and analyze the relationship
-5/4…. 1/2 …. 7

5. I. 3x2 + 16x + 20 = 0
II. 3y2 – 14y – 5 = 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 + 16x + 20 = 0
3x2 + 6x + 10x + 20 = 0
Gives x = -2, -10/3
3y2 – 14y – 5 = 0
3y2 – 15y + y – 5 = 0
Gives y = -1/3, 5
Put all values on number line and analyze the relationship
-10/3… -2…. -1/3…. 5

6. I. 3x2 + 7x – 6 = 0
II. 6y2 – 35y + 50 = 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 + 7x – 6 = 0
3x2 + 9x – 2x – 6 = 0
Gives x = -3, 2/3
6y2 – 35y + 50 = 0
6y2 – 15y – 20y + 50 = 0
Gives y = 5/2, 10/3
Put all values on number line and analyze the relationship
-3… 2/3… 5/2…. 10/3

7. I. 7x2 – 11x – 6 = 0
II. 6y2 + 13y + 5 = 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:

7x2 – 11x – 6 = 0
7x2 – 14x + 3x – 6 = 0
Gives x = -3/7, 2
6y2 + 13y + 5 = 0
6y2 + 3y + 10y + 5 = 0
Gives y = -5/3, -1/2
Put all values on number line and analyze the relationship
-5/3…. -1/2…. -3/7….. 2

8. I. 3x2 + 4x – 39 = 0
II. 3y2 – 5y – 78 = 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 + 4x – 39 = 0
3x2 – 9x + 13x – 39 = 0
Gives x = -13/3, 3
3y2 – 5y – 78 = 0
3y2 – 18y + 13y – 78 = 0
Gives y = -13/3, 6
Put all values on number line and analyze the relationship
-13/3…. 3…. 6

9. I. 4x2 + 13x + 9 = 0
II. 3y2 – 7y – 20 = 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 + 13x + 9 = 0
4x2 + 4x + 9x + 9 = 0
Gives x = -9/4, -1
3y2 – 7y – 20 = 0
3y2 – 12y + 5y – 20 = 0
Gives y = -5/3, 4
Put all values on number line and analyze the relationship
-9/4…. -5/3…. -1….4

10. I. 4x2 + 13x + 10 = 0
II. 4y2 – 7y – 15 = 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 + 13x + 10 = 0
4x2 + 8x + 5x + 10 = 0
Gives x = -2, -5/4
4y2 – 7y – 15 = 0
4y2 – 12y + 5y – 15 = 0
Gives y = -5/4, 3
Put all values on number line and analyze the relationship
-2… -5/4…. 3