# Quadratic Equations Set – 23

1. I. 7x2 – 9x + 2 = 0
II. y2 – 4y + 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

Option D
Solution:
I. 7x2– 7x – 2x + 2 = 0
or, 7x(x – 1) – 2(x – 1) = 0
(7x – 2) (x – 1) = 0
or, x =2/7 , 1
II. y2– y – 3y + 3 = 0
or, y(y – 1) – 3(y – 1) = 0
or, (y – 3) (y – 1) = 0
y = 1, 3
x <= y

2. I. x2+ x – 20 = 0
II. 2y2 – 19y + 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 B
Solution:
I. x2+ x – 20 = 0
or, x2+ 5x – 4x – 20 = 0
or, x(x + 5) – 4(x + 5) = 0
or, (x – 4) (x + 5) = 0
x = 4, – 5
II. 2y2– 10y – 9y + 45 = 0
or, 2y(y – 5) – 9(y – 5) = 0
or, (y – 5) (2y – 9) = 0
y = 5 , 9/2

3. I. 7x + 3y = 26
II. 2x + 17y = -41
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:
Eqn (I) × 2
Eqn (II) × 7
14x + 6y = 52
14x + 119y = – 287
– 113y = 339
y = – 3 and x = 5, ie x > y

4. I. 3x2 – 20x + 33 = 0
II. 2y2 – 11y + 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

Option C
Solution:
I. 3x2– 9x – 11x + 33 = 0
or, 3x(x – 3) – 11(x – 3) = 0
or, (3x – 11) (x – 3) = 0
x = 3, 11/3
II. 2y2– 6y – 5y + 15 = 0
or, 2y(y – 3) – 5(y – 3) = 0
or, (y – 3) (2y – 5) = 0
y = 3 , 5/2

5. I. 5x2 + 2x – 3 = 0
II. 2y2+ 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

Option A
Solution:
5x2+ 5x – 3x – 3 = 0
or 5x (x + 1) – 3(x + 1) = 0
or (5x – 3) (x + 1) = 0
x= 3/5, -1
II. 2y2+ 4x + 3y + 6 = 0
or 2y(y + 2) + 3(y + 2) =0
or (2y + 3) (y + 2) = 0
y = -3/2 , -2

6. I. 35x2 – 53x + 20 = 0
II. 56y2 -97y + 42 = 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:
I. 35x2 – 28x – 25x + 20 = 0
or 7x(5x – 4) – 5(5x – 4) = 0
or (7x – 5) (5x – 4) = 0
x  5/7 , 4/5
II. 56y2 – 48y – 49y + 42 = 0
or 8y(7y – 6) – 7(7y – 6) = 0
or (8y – 7) (7y – 6) = 0
y = 7/8 , 6/7

7. I. x = 3√4913
II. 13y + 3x = 246
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:
I. x = 3√4913
x = 17

II. 13y = 246 – 3x
or 13y = 246 – 51 = 195
y = 15
x > y

8. I. x2 – 5x – 14 = 0
II. y2+ 7y + 10 = 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 C
Solution:
I. x2– 7x + 2x – 14 = 0
or x(x – 7) + 2(x – 7) = 0
(x + 2) (x – 7) = 0
x = -2, 7
II. y2+ 5y + 2y + 10 = 0
or y(y + 5) + 2(y + 5) = 0
or (y + 2) (y + 5) = 0
y = -2, -5
x ≥  y

9. I. x2= 64
II. 2y2 + 25y + 72 = 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:
I. x2= 64
x = ±8
II. 2y2+ 9y + 16y + 72 = 0
or, y(2y + 9) + 8(2y + 9) = 0
or, (y + 8) (2y + 9) = 0
y = -8 , -9/2
no relation between x and y.

10. I. x2 – 3481 = 0
II. 3y2 = 3216000
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