Quadratic Equations Set – 10

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. 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

 

3. 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

 

4. 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

 

5. I. 6x2 + 5x – 1 = 0,
II. 3y2 – 11y + 6 = 0
A) If X > Y
B) If X < Y
C) If X ≥ Y
D) If X ≤ Y
E) If X = Y or relation cannot be established

Answer & Explanation

 Option B
Solution: 

6x2 + 5x – 1 = 0
6x2 + 6x – x – 1 = 0
Gives x = -1, 1/6
3y2 – 11y + 6 = 0
3y2 – 9y – 2y + 6 = 0
Gives y = 2/3, 3
Put on number line
-1… 1/6… 2/3… 3

 

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

Answer & Explanation

 Option E
Solution: 

3x2 + 4x – 4 = 0
3x2 + 6x – 2x – 4 = 0
Gives x = -2, 2/3
4y2 + 5y – 6 = 0
4y2 + 5y – 6 = 0
Gives y = -2, 3/4
Put on number line
-2…. 2/3… 3/4
When x=2/3, x>y(= -2) and x<y(= 3/4)
So cant be determined

 

7. I. 5x2 – 36x – 32 = 0,
II. 3y2 – 17y – 6 = 0
A) If X > Y
B) If X < Y
C) If X ≥ Y
D) If X ≤ Y
E) If X = Y or relation cannot be established

Answer & Explanation

 Option E
Solution: 

5x2 – 36x – 32 = 0
5x2 + 4x – 40x – 32 = 0
Gives x = -4/5, 8
3y2 – 17y – 6 = 0
3y2 + y – 18y – 6 = 0
Gives y= -1/3, 6
Put on number line
-4/5…. -1/3… 6… 8

 

8. I. 3x2 – 25x + 52 = 0,
II. 15y2 – 38y – 40 = 0
A) If X > Y
B) If X < Y
C) If X ≥ Y
D) If X ≤ Y
E) If X = Y or relation cannot be established

Answer & Explanation

 Option A
Solution: 

3x2 – 25x + 52 = 0
3x2 – 12x – 13x + 52 = 0
Gives x = 4, 13/3
15y2 – 38y – 40 = 0
15y2 + 12y – 50y – 40 = 0
Gives y = -4/5, 10/3
Put on number line
-4/5… 10/3… 4… 13/3

 

9. I. 6x2 + x – 2 = 0,
II. 2y2 + 11y + 14 = 0
A) If X > Y
B) If X < Y
C) If X ≥ Y
D) If X ≤ Y
E) If X = Y or relation cannot be established

Answer & Explanation

 Option A
Solution: 

6x2 + x – 2 = 0
6x2 + 4x – 3x – 2 = 0
Gives x = -2/3, 1/2
2y2 + 11y + 14 = 0
2y2 + 4y + 7y + 14 = 0
Gives y = -7/2, -2

 

10. I. 3x2 + 14x – 5 = 0,
II. 3y2 – 19y + 6 = 0
A) If X > Y
B) If X < Y
C) If X ≥ Y
D) If X ≤ Y
E) If X = Y or relation cannot be established

Answer & Explanation

 Option D
Solution: 

3x2 + 14x – 5 = 0
3x2 + 15x – x – 5 = 0
Gives x = -5, 1/3
3y2 – 19y + 6 = 0
3y2 – 18y – y + 6 = 0
Gives y = 1/3, 6
Put on number line
-5…. 1/3… 6

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