Quadratic Equations Set – 2

1. I. 4x2 + 27x + 18 = 0,
II. 2y2 – 7y + 3 = 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 + 27x + 18 = 0
4x2 + 24x + 3x + 18 = 0
So x = -3/4, -6
2y2 – 7y + 3 = 0
2y2 – 6y – y + 3 = 0
So y = 1/2, 3
Put all values on number line and analyze the relationship
-6… -3/4… 1/2… 3

 

2. I. 3x2 – 2x – 8 = 0,
II. 6y2 – 17y + 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 D
Solution: 

3x2 – 2x – 8 = 0
3x2 – 6x + 4x – 8 = 0
So x = -4/3, 2
6y2 – 17y + 10 = 0
6y2 – 12y – 5y + 10 = 0
So y = 5/6, 2
Put all values on number line and analyze the relationship
-4/3… 2… 5/6

 

3. I. 32 + 11x + 6 = 0,
II. 5y2 + 16y + 3 = 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: 

32 + 11x + 6 = 0
32 + 9x + 2x + 6 = 0
So x = -3, -2/3
5y2 + 16y + 3 = 0
5y2 + 15y + y + 3 = 0
So y = -1/5, -3
Put all values on number line and analyze the relationship
-3 …. -2/3 ….-1/5
Since the common value (-3) is not in between other 2 values, there is no relationship between x and y.

 

4. I. 4x2 – 11x + 6 = 0,
II. 6y2 – 29y + 28 = 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 – 11x + 6 = 0
4x2 – 8x – 3x + 6 = 0
So x = 3/4, 2
6y2 – 29y + 28 = 0
6y2 – 8y – 21y + 28 = 0
So y = 4/3, 7/2
Put all values on number line and analyze the relationship
3/4 …. 4/3….. 2…. 7/2

 

5. I. 3x2 – 25x + 52 = 0,
II. 3y2 – 8y – 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 – 25x + 52 = 0
3x2 – 12x – 13x + 52 = 0
So x = 4, 13/3
3y2 – 8y – 16 = 0
3y2 – 12y + 4y – 16 = 0
So y = 4, -4/3
Put all values on number line and analyze the relationship
-4/3 …. 4…. 13/3

 

6. I. 8x2 + 10x + 3 = 0,
II. 3y2 + 70y + 40 = 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: 

8x2 + 10x + 3 = 0
8x2 + 4x + 6x + 3 = 0
So x = -3/4, -1/2
3y2 + 70y + 40 = 0
3y2 + 30y + 40y + 40 = 0
So y = -10, -4/3
Put all values on number line and analyze the relationship
-10 … -4/3 …. -3/4 …. -1/2

 

7. I. 50x2 ¬¬– 95x + 42 = 0,
II. 50y2 – 65y + 21 = 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: 

50x2 ¬¬– 95x + 42 = 0
50x2 ¬¬– 60x – 35x + 42 = 0
So x = 7/10, 6/5
50y2 – 65y + 21 = 0
50y2 – 65y + 21 = 0
So y = 3/5, 7/10
Put all values on number line and analyze the relationship
3/5…. 7/10…. 6/5

 

8. I. 5x2 – 13x + 6 = 0,
II. 3y2 – 22y – 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 B
Solution: 

5x2 – 13x + 6 = 0
5x2 – 10x – 3x + 6 = 0
So x = 3/5, 2
3y2 – 22y – 35 = 0
3y2 – 15y – 7y – 35 = 0
So y = 7/3, 5
Put all values on number line and analyze the relationship
3/5…. 2…. 7/3… 5

 

9. I. 3x2 – 4x – 15 = 0,
II. 5y2 – 11y – 18 = 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 – 15 = 0
3x2 – 9x + 5x – 15 = 0
So x = -5/3, 3
5y2 – 11y – 18 = 0
5y2 – 15y + 6y – 18 = 0
So y = -6/5, 3
Put all values on number line and analyze the relationship
-5/3….. -6/5…. 3
Since the common value (3) is not in between other 2 values, there is no relationship between x and y.

 

10. I. 2x2 + 5x – 12 = 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: 

2x2 + 5x ¬– 12 = 0
2x2 + 8x ¬– 3x – 12 = 0
So x = -4 , 3/2
2y2 – 19y + 35 = 0
2y2 – 14y – 5y + 35 = 0
So y = 5/2, 7
Put all values on number line and analyze the relationship
-4……. 3/2…… 5/2…

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