Quadratic Equations Set – 1

1. I. 20x2 – 31x + 12 = 0,
II. 6y2 – 7y + 2 = 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

 A) If x > y
Solution: 

20x2 – 31x + 12 = 0
20x2 – 16x – 15x + 12 = 0
So x = 3/4, 4/5
6y2 – 7y + 2 = 0
6y2 – 3y – 4y + 2 = 0
So y = 1/2, 2/3
Put on number line
1/2… 2/3… 3/4… 4/5

 

2. I. 3x2 + 22 x + 24 = 0,
II. 3y2 – 10y + 3 = 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

 B) If x < y
Solution: 

3x2 + 22 x + 24 = 0
3x2 + 18x + 4x + 24 = 0
So x = -4/3, -6
3y2 – 10y + 3 = 0
3y2 – 9y – y + 3 = 0
So y = 1/3, 3
Put on number line
-6… -4/3… 1/3… 3

 

3. I. 6x2 – x – 2 = 0,
II. 5y2 – 18y + 9 = 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

 E) If x = y or relation cannot be established
Solution: 

6x2 – x – 2 = 0
6x2 + 3x – 4x – 2 = 0
So x = -1/2, 2/3
5y2 – 18y + 9 = 0
5y2 – 15y – 3y + 9 = 0
So y = 3/5, 3
Put on number line
-1/2 …. 3/5 ….2/3 …. 3

 

4. I. x2 – x – 6 = 0,
II. 5y2 – 7y – 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

 E) If x = y or relation cannot be established
Solution: 

x2 – x – 6 = 0
x2 – 2x + 3x – 6 = 0
So x = -3, 2
5y2 – 7y – 6 = 0
5y2 – 10y + 3y – 6 = 0
So y = -3/5, 2
Put on number line
-3 …. -3/5….. 2

 

5. I. 3x2 – 10x + 8 = 0,
II. 3y2 + 8y – 16 = 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

 C) If x ≥ y
Solution: 

3x2 – 10x + 8 = 0
3x2 – 6x – 4x + 8 = 0
So x = 2, 4/3
3y2 + 8y – 16 = 0
3y2 + 12y – 4y – 16 = 0
So y = -4, 4/3
Put on number line
-4 …. 4/3…. 2

 

6. I. 2x2 + 17x + 30 = 0,
II. 2y2 + 13y + 18 = 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

 E) If x = y or cannot be established
Solution: 

2x2 + 17x + 30 = 0
2x2 + 12x + 5x + 30 = 0
So x = -6, -5/2
2y2 + 13y + 18 = 0
2y2 + 4y + 9y + 18 = 0
So y = -9/2, -2
Put on number line
-6 … -9/2 …. -5/2 …. -2

 

7. I. 3x2 + 16x + 20 = 0,
II. 3y2 + 8y + 4 = 0 

A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relationship cannot be determined

Answer & Explanation

 D) If x ≤ y
Solution: 

3x2 + 16x + 20 = 0
3x2 + 6x + 10x + 20 = 0
So x = -10/3, -2
3y2 + 8y + 4 = 0
3y2 + 6y + 2y + 4 = 0
So y = -2, -2/3
put on number line
-10/3…. -2…. -2/3

 

8. I. x2 + x – 20 = 0,
II. 2y2 + 13y + 15 = 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

 E) If x = y or relation cannot be established
Solution: 

x2 + x – 20 = 0
(x+5)(x-4) = 0
So x = -5, 4
2y2 + 13y + 15 = 0
2y2 + 10y + 3y + 15 = 0
So y = -5, -3/2
Put on number line
-5…. -3/2…. 4

 

9. I. 5x2 – 7x – 6 = 0,
II. 5y2 + 23y + 12 = 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

 C) If x ≥ y
Solution: 

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

 

10. I. 2x2 – 9x + 4 = 0,
II. 2y2 + 7y – 4 = 0 

A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relationship cannot be determined

Answer & Explanation

 C) If x ≥ y
Solution: 

2x2 – 9x + 4 = 0
2x2 – 8x – x + 4 = 0
So x = 4 , 1/2
2y2 + 7y – 4 = 0
2y2 + 8y – y – 4 = 0
So y = -4, 1/2
Put on number line
-4……. 1/2…… 4

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