Quadratic Equations Set – 9

1. I. 8/√x + 9/(√x +1) = 7,
II. 9/√y – 3/√y = 2
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: 

8/√x + 9/(√x +1) = 7
[8(√x +1) + 9√x]/[√x * (√x +1)] = 7
17√x + 8 = 7 (x + √x)
7x – 10√x – 8 = 0
7x – 14√x + 4√x – 8 = 0
7√x (√x – 2) + 4 (√x – 2) = 0
√x cannot be -4/7
So √x = 2, so x = 4
9/√y – 3/√y = 2
(9 – 3)/√y = 2
Gives √y = 3, so y = 9

 

2. I. 9/√x + 3/√x = √x + 1,
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 A
Solution: 

9/√x + 3/√x = √x + 1
12/√x = √x + 1
x + √x – 12 = 0
x + 4√x – 3√x – 12 = 0
√x(√x + 4) – 3 (√x + 4) = 0
√x cannot be -4, So √x = 3 => x = 9
4y2 + 5y – 6 = 0
4y2 + 5y – 6 = 0
Gives y = -2, 3/4
Put all values on number line and analyze the relationship
-2… 3/4… 9

 

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

6x2 + 13x + 6 = 0
6x2 + 9x + 4x + 6 = 0
Gives x = -2/3, -3/2
6y2 – y – 2 = 0
6y2 + 3y – 4y – 2 = 0
Gives y = -1/2, 2/3
Put all values on number line and analyze the relationship
-3/2… -2/3… -1/2… 2/3

 

4. I. 3x2 + 14x – 5 = 0,
II. 3y2 – 11y + 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 + 14x – 5 = 0
3x2 + 15x – x – 5 = 0
Gives x = -5, 1/3
3y2 – 11y + 6 = 0
3y2 – 9y – 2y + 6 = 0
Gives y = 2/3, 3
Put all values on number line and analyze the relationship
-5… 1/3… 2/3… 3

 

5. I. 6x2 + 5x – 1 = 0,
II. 3y2 – 10y + 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: 

6x2 + 5x – 1 = 0
6x2 + 6x – x – 1 = 0
Gives x = -1, 1/6
3y2 – 10y + 3 = 0
3y2 – 9y – y + 3 = 0
Gives y = 1/3, 3
Put all values on number line and analyze the relationship
-1… 1/6… 1/3… 3

 

6. I. 12x2 – 5x – 3 = 0,
II. 3y2 – 11y + 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: 

12x2 – 5x – 3 = 0
12x2 + 4x – 9x – 3 = 0
Gives x = -1/3, 3/4
3y2 – 11y + 6 = 0
3y2 – 9y – 2y + 6 = 0
Gives y = 2/3, 3
Put all values on number line and analyze the relationship
-1/3… 2/3… 3/4… 3

 

7. I. 6x2 + 7x + 2 = 0,
II. 15y2 – 38y – 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 E
Solution: 

6x2 + 7x + 2 = 0
6x2 + 4x + 3x + 2 = 0
Gives x = -2/3, -1/2
15y2 – 38y – 40 = 0
15y2 + 12y – 50y – 40 = 0
Gives y = -4/5, 10/3
Put all values on number line and analyze the relationship
-4/5… -2/3… -1/2… 10/3

 

8. I. 3x2 – 25x + 52 = 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 A
Solution: 

3x2 – 25x + 52 = 0
3x2 – 12x – 13x + 52 = 0
Gives x = 4, 13/3
2y2 – 7y + 3 = 0
2y2 – 6y – y + 3 = 0
So y = 1/2, 3
Put all values on number line and analyze the relationship
1/2… 3… 4… 13/3

 

9. I. x2 = 1156,
II. y = √1156
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: 

x2 = 1156,
So x = -34, 34
y = √1156
So y = 34
Put all values on number line and analyze the relationship
-34… 34

 

10. I. x2 – √3969 = √6561,
II. y2 – √1296 = √4096
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: 

x2 – √3969 = √6561
x2 – 63 = 81
x2 = 144
So x = -12, 12
y2 – √1296 = √4096
y2 – 36 = 64
y2 = 100
So y = -10, 10
Put all values on number line and analyze the relationship
-12… -10….10…. 12

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