Quadratic Equations Set – 3

1. I. 3x2 + 20x + 32 = 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 + 20x + 32 = 0
3x2 + 12x + 8x + 32 = 0
So x = -4, -8/3
3y2 – 4y – 4 = 0
3y2 – 6y + 2y – 4 = 0
So y = -2/3, 2
Put all values on number line and analyze the relationship
-4… -8/3… -2/3… 2

 

2. I. 4x2 – 12x + 5 = 0,
II. 6y2 – 13y + 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: 

4x2 – 12x + 5 = 0
4x2 – 2x – 10x + 5 = 0
So x = ½, 5/2
6y2 – 13y + 6 = 0
6y2 – 4y – 9y + 6 = 0
So y = 2/3, 3/2
Put all values on number line and analyze the relationship
1/2… 2/3… 3/2…. 5/2

 

3. I. 32 – 14x + 16 = 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: 

32 – 14x + 16 = 0
32 – 6x – 8x + 16 = 0
So x = 8/3, 2
4y2 – 5y – 6 = 0
4y2 – 8y + 3y – 6 = 0
So y = -3/4, 2
Put all values on number line and analyze the relationship
-3/4 …. 2 ….8/3

 

4. I. 5x2 – 8x – 4 = 0,
II. 5y2 – 23y – 10 = 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: 

5x2 – 8x – 4 = 0
5x2 – 10x + 2x – 4 = 0
So x = -2/5, 2
5y2 – 23y – 10 = 0
5y2 – 25y + 2y – 10 = 0
So y = -2/5, 5
Put all values on number line and analyze the relationship
-2/5 …. 2….. 5

 

5. I. 3x2 + 13x + 14 = 0,
II. 4y2 + 9y + 2 = 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 + 13x + 14 = 0
3x2 + 6x + 7x + 14 = 0
So x = -7/3, -2
4y2 + 9y + 2 = 0
4y2 + 8y + y + 2 = 0
So y = -2, -1/4
Put all values on number line and analyze the relationship
-7/3 …. -2…. -1/4

 

6. I. 3x2 + 8x + 5 = 0,
II. 5y2 – 7y – 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 B
Solution: 

3x2 + 8x + 5 = 0
3x2 + 3x + 5x + 5 = 0
So x = -5/3, -1
5y2 – 7y – 6 = 0
5y2 – 7y – 6 = 0
So y = -3/5, 2
Put all values on number line and analyze the relationship
-5/3…. -1…. -3/5…. 2

 

7. I. 3x2 ¬¬+ 16x + 20 = 0,
II. 3y2 + 14y + 16 = 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: 

3x2 ¬¬+ 16x + 20 = 0
3x2 ¬¬+ 6x + 10x + 20 = 0
So x = -10/3, -2
3y2 + 14y + 16 = 0
3y2 + 6y + 8y + 16 = 0
So y = -8/3, -2
Put all values on number line and analyze the relationship
-10/3…. -8/3…. -2

 

8. I. 4x2 – 9x + 2 = 0,
II. 3y2 – 16y + 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 B
Solution: 

4x2 – 9x + 2 = 0
4x2 – 8x – x + 2 = 0
So x = 1/4, 2
3y2 – 16y + 21 = 0
3y2 – 9y – 7y + 21 = 0
So y = 7/3, 3
Put all values on number line and analyze the relationship
1/4…. 2…. 7/3… 3

 

9. I. 3x2 + 5x + 2 = 0,
II. 3y2 + 11y + 10 = 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: 

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

 

10. I. 4x2 – 9x + 2 = 0,
II. 2y2 – 19y + 35 = 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: 

4x2 – 9x + 2 = 0
4x2 – 8x – x + 2 = 0
So x = 1/4, 2
2y2 – 19y + 35 = 0
2y2 – 14y – 5y + 35 = 0
So y = 5/2, 7
Put all values on number line and analyze the relationship
1/4……. 2…… 5/2…7

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