Quadratic Equations Set – 12

1. I. 20x2 – 31x + 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 B
Solution: 

20x2 – 31x + 12 = 0
20x2 – 16x – 15x + 12 = 0
So x = 3/4, 4/5
3y2 – 16y + 16 = 0
3y2 – 14y – 4y + 16 = 0
Gives y = 4, 4/3

 

2. I. 3x2 + 22 x + 24 = 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

Answer & Explanation

 Option E
Solution: 

3x2 + 22 x + 24 = 0
3x2 + 18x + 4x + 24 = 0
So x = -4/3, -6
2y2 – 5y – 12 = 0
2y2 – 8y + 3y – 12 = 0
Gives y = -3/2, 4

 

3. I. 2x2 – 9x + 4 = 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

Answer & Explanation

 Option E
Solution: 

Solution:
2x2 – 9x + 4 = 0
2x2 – 8x – x + 4 = 0
So x = 4 , 1/2
4y2 – 13y – 12 = 0
4y2 – 16y + 3y – 12 = 0
Gives y = -3/4, 4

 

4. I. 5x2 + 23x + 12 = 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 D
Solution: 

5x2 + 23x + 12 = 0
5x2 + 20x + 3x + 12 = 0
So x = -4, -3/5
5y2 – 7y – 6 = 0
5y2 – 10y + 3y – 6 = 0
So y = -3/5, 2
Put all values on number line and analyze the relationship
-4….. -3/5…. 2

 

5. I. 7x2 + 19x – 6 = 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: 

7x2 + 19x – 6 = 0
7x2 + 21x – 2x – 6 = 0
Gives x = -3, 2/7
2y2 – 7y + 3 = 0
2y2 – 6y – y + 3 = 0
So y = 1/2, 3

 

6. I. 4x2 – 12x + 5 = 0,
II. 2y2 – 19y + 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 D
4x2 – 12x + 5 = 0
4x2 – 2x – 10x + 5 = 0
x = 1/2, 5/2
2y2 – 19y + 35 = 0
2y2 – 14y – 5y + 35 = 0
So y = 5/2, 7

 

7. I. 2x2 + 5x ¬– 12 = 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

Answer & Explanation

 Option E
2x2 + 5x ¬– 12 = 0
2x2 + 8x ¬– 3x – 12 = 0
So x = -4 , 3/2
4y2 + 13y – 12 = 0
4y2 + 16y – 3y – 12 = 0
y = -4, 3/4

 

8. I. 3x2 + 22x + 24 = 0,
II. 4y2 – 9y – 9 = 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
3x2 + 22 x + 24 = 0
3x2 + 18x + 4x + 24 = 0
Gives x = -4/3, -6
4y2 – 9y – 9 = 0
4y2 – 12y + 3y – 9 = 0
y = -3/4, 3

 

9. I. 20x2 – 31x + 12 = 0,
II. 4y2 + 9y – 9 = 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
20x2 – 31x + 12 = 0
20x2 – 16x – 15x + 12 = 0
Gives x = 3/4, 4/5
4y2 + 9y – 9 = 0
4y2 + 12y – 3y – 9 = 0
y = 3/4, -3

 

10. I. 6x2 – 7x – 3 = 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: 

6x2 – 7x – 3 = 0
6x2 + 2x – 9x – 3 = 0
Gives x = -1/3, 3/2
4y2 + 5y – 6 = 0
4y2 + 8y – 3y – 6 = 0
Gives y = -2, 3/4

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