# Aptitude Questions: Quadratic Equations Set 12

Hello Aspirants. Welcome to Online Quantitative Aptitude Section in AffairsCloud.com. Here we are creating sample questions in Quadratic Equations which is common for all the competitive exams. We have included Some questions that are repeatedly asked in bank exams !!!

You have to solve equation I and II ,Give answer
A) If X > Y
B) If X < Y
C) If X ≥ Y
D) If X ≤ Y
E) If X = Y or cannot be established

1. x2 – 18x + 72= 0,
3y2 + 7y + 4 = 0

A) If X > Y
Explanation:

x2 – 18x + 72= 0
(x-12)(x-6) = 0
x = 6, 12
3y2 + 7y + 4 = 0
(y+1)(3y+4) = 0
y = -1, -4/3
Put on number line
-4/3        -1               6               12

2. x2 = 4,
y2 + y – 6 = 0

E) If X = Y or cannot be established
Explanation:

x2 = 4
x = 2 , -2
y2 + y – 6 = 0
(y+3)(y-2) = 0
y = -3, 2
put on number line
-3                     -2                   2
When y = -3, y < x
When y = 2, y ≥ x
So no relation

3. 2x2 + x – 36 = 0,
2y2 – 13y + 20 = 0

E) If X = Y or cannot be established
Explanation:

2x2 + x – 36 = 0
2x2 – 8x + 9x – 36 = 0
x = 4 , -9/2
2y2 – 13y + 20 = 0
2y2 – 8y – 5y +20 = 0
2y(y-4) – 5(y-4) = 0
y = 4, 5/2
put on number line
-9/2                     5/2                         4

4. x2 – 5x = 0,
2y2 + 7y – 4 = 0

E) If X = Y or cannot be established
Explanation:

x2 – 5x = 0
x(x-5) = 0
x = 0, 5
2y2 + 7y – 4 = 0
2y2 + 8y – y – 4 = 0
y = -4, 1/2
put on number line
-4               0                    1/2                    5

5. 2x2 + 5x + 2= 0,
2y2 + 19y + 45 = 0

A) If X > Y
Explanation:

2x2 + 5x + 2= 0
(2x+1)(x+2) =0
X= -1/2, -2
2y2 + 19y + 45 = 0
(2y+10)(2y+9) = 0
Y= -10/2, -9/2 = -5, -4.5
Put on number line
-5                  -4.5                      -2                        -1/2

6. x2 + x – 20 = 0,
y2 – 13y + 40 = 0

B) If X < Y
Explanation:

x2 + x – 20 = 0
(x+5)(x-4) = 0
x = -5, 4
y2 – 13y + 40 = 0
(y-5)(y-8) = 0
y = 5, 8

7. x2 – 11x + 24 = 0,
y2 + 9y + 18 = 0

A) If X > Y
Explanation:

x2 – 11x + 24 = 0
(x-3)(x-8) = 0
x = 3, 8
y2 + 9y + 18 = 0
(y+3)(y+6) = 0
y = -3, -6
put on number line
-6                -3                  3                      8

8. 3x2 + 8x + 5 = 0,
2y2 + y – 1 = 0

D) If X ≤ Y
Explanation:

3x2 + 8x + 5 = 0
3x2 + 3x + 5x + 5 = 0
x = -1, -5/3
2y2 + y – 1 = 0
2y2 + 2y – y -1 = 0
y = -1, 1/2
put on number line
-5/3                     -1                   1/2

9. 3x + 2y = 16,
2x+ 3y = 33/2

B) If X < Y
Explanation:

Solve the equations, x = 3, y = 3.5

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

C) If X ≥ Y
Explanation:

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

AffairsCloud Recommends Oliveboard Mock Test

AffairsCloud Ebook - Support Us to Grow