# Quadratic Equations Set – 14

1. I. 3x2 + 22x + 24 = 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

Option D
Solution:

3x2 + 22 x + 24 = 0
3x2 + 18x + 4x + 24 = 0
Gives x = -4/3, -6
3y2 – 8y – 16 = 0
3y2 – 12y + 4y – 16 = 0
So y = -4/3, 4
Plot on number line
-6…. -4/3……. 4

2. I. 5x2 – 18x – 8 = 0,
II. 2y2 + 11y + 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

Option A
Solution:

5x2 – 18x – 8 = 0
5x2 – 20x + 2x – 8 = 0
So x = -2/5, 4
2y2 + 11y + 12 = 0
2y2 + 8y + 3y + 12 = 0
Gives y = -4, -3/2
Plot on number line
-4… -3/2…. -2/5….. 4

3. I. x2 – 652 = 504,
II. y = √1156
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

Option D
Solution:

x2 – 652 = 504
x2 = 1156
So x = 34, -34
y = √1156 = 34
Plot on number line
-34… 34

4. I. 9/√x + 8/(√x +1) = 5,
II. 12/√y – 4/√y = 2
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

Option B
Solution:

9/√x + 8/(√x +1) = 5
[9(√x +1) + 8√x]/[√x * (√x +1)] = 5
17√x + 9 = 5 (x + √x)
5x – 12√x – 9 = 0
5x – 15√x + 3√x – 9 = 0
5√x (√x – 3) + 3 (√x – 3) = 0
√x cannot be -3/3
So √x = 3, so x = 9
12/√y – 4/√y = 2
8/√y = 2
So √y = 4 or y = 16
So y > x

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

Option E
Solution:

3x2 – 6x – √3x + 2√3 = 0
3x (x- 2) – √3 (x – 2) = 0,
So x = 2, √3/3
2y2 – 3y – 2√2y + 3√2 = 0
y (2y – 3) – √2 (2y – 3) = 0
So y = 3/2, √2 (1.44)
plot on number line
√3/3(0.57)…….√2…..(3/2)……2

6. I. x2 – 2x – √5x + 2√5 = 0
II. y2 – 3y – √6y + 3√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

Option B
Solution:

x2 – 2x – √5x + 2√5 = 0
x (x – 2) – √5 (x – 2) = 0
So x = 2, √5 (2.23)
y2 – 3y – √6y + 3√6 = 0
y (y – 3) – √6 (y – 3) = 0
So y = 3, √6 (2.44)
Plot on number line
2…2.23……2.44…….3

7. I. 8x2 + 6x + 1 = 0,
II. 5y2 + 8y – 4 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relationship cannot be determined

Option E
Solution:

8x2 + 6x + 1 = 0
8x2 + 4x + 2x + 1 = 0
So x = -1/4, -1/2
5y2 + 8y – 4 = 0
5y2 + 10y – 2y – 4 = 0
So y = -2, 2/5

8. I. 4x2 – 23x + 30 = 0,
II. 4y2 – 3y – 45 = 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

Option E
Solution:

4x2 – 23x + 30 = 0
4x2 – 15x – 8x + 30 = 0
So x = 15/4, 2
4y2 – 3y – 45 = 0
4y2 + 12y – 15y – 45 = 0
So y = -3, 15/4
Put on number line
-3…. 2…. 15/4

9. I. 5x2 – 7x – 6 = 0,
II. 3y2 – 2y – 8 = 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

Option E
Solution:

5x2 – 7x – 6 = 0
5x2 – 10x + 3x – 6 = 0
So x = -3/5, 2
3y2 – 2y – 8 = 0
3y2 – 6y + 4y – 8 = 0
So y = -4/3, 1
Plot on number line
-4/3……-3/5….. 1….. 2

10. I. 3x2 + 2x – 21 = 0,
II. 3y2 – 19y + 28 = 0
A) x > y
B) x < y
C) x ≥ y
D) x ≤ y
E) x = y or relationship cannot be determined