Aptitude Questions: Quadratic Equations Set 16

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 !!!

1. 6x2 – x – 2 = 0, 4y2 – 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
E) If X = Y or relation cannot be established
Explanation:

6x2 – x – 2 = 0
6x2 + 3x – 4x – 2 = 0
Gives x = -1/2, 2/3
4y2 – 4y – 3 = 0
4y2 + 2y – 6y – 3 = 0
Gives y = -1/2, 3/2
Put on number line
-1/2        2/3           3/2
When x = -1/2, y ≥ x
When x = 2/3 y(-1/2) < x, and y(3/2) > x
So relation cannot be determined

2. 3x2 – 4x – 4 = 0, 2y2 – 9y + 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
D) If X ≤ Y
Explanation:

3x2 – 4x – 4 = 0
3x2 + 2x – 6x – 4 = 0
Gives x = -2/3 , 2
2y2 – 9y + 10 = 0
2y2 – 4y – 5y + 10 = 0
Gives y = 2, 5/2
Put on number line
-2/3       2            5/2

3. 5x2 – 13x – 6 = 0, 3y2 + 14y + 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
A) If X > Y
Explanation:

5x2 – 13x – 6 = 0
5x2 + 2x – 15x – 6 = 0
Gives x = -2/5, 3
3y2 + 14y + 8 = 0
3y2 + 12y + 2y + 8 = 0
Gives y = -4, -2/3
Put on number line
-4       -2/3          2/5              3

4. 2x2 + 17x + 30 = 0, 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
E) If X=Y or cannot be established
Explanation:

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

5. 4x2 + 23x + 15 = 0, 4y2 – 11y + 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
B) If X < Y
Explanation:

4x2 + 23x + 15 = 0
4x2 + 20x + 3x + 15 = 0
Gives x = -5, -3/4
4y2 – 11y + 6 = 0
4y2 – 8y – 3y + 6 = 0
Gives y= 3/4 2
Put on number line
-5        -3/4          3/4            2

6. 4x2 + 13x + 3 = 0, 4y2 – 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
D) If X ≤ Y
Explanation:

4x2 + 13x + 3 = 0
4x2 + 12x + x + 3 = 0
Gives x = -3, -1/4
4y2 – 7y – 2 = 0
4y2 – 8y + y – 2 = 0
Gives y = -1/4 2
Put on number line
-3           -1/4          2

7. x2 + x – 6 = 0, 4y2 + 13y + 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
E) If X = Y or relation cannot be established
Explanation:

x2 + x – 6 = 0
x2 – 2x + 3x – 6 = 0
Gives x = -3, 2
4y2 + 13y + 3 = 0
4y2 + 12y + y + 3 = 0
Gives y = -3, -1/4
Put on number line
-3           -1/4          2

8. 3x2 + 4x – 7 = 0, 3y2 + 5y – 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
E) If X = Y or relation cannot be established
Explanation:

3x2 + 4x – 7 = 0
3x2 + 7x – 3x – 7 = 0
Gives x = -7/3, 1
3y2 + 5y – 2 = 0
3y2 + 6y – y – 2 = 0
Gives y = -2, 1/3
Put on number line
-7/3         -2          1/3           1

9. 3x2 – 10x + 8 = 0, 3y2 + 14y + 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
A) If X > Y
Explanation:

3x2 – 10x + 8 = 0
3x2 – 6x – 4x + 8 = 0
Gives x = 2, 4/3
3y2 + 14y + 16 = 0
3y2 + 6y + 8y + 16 = 0
Gives y = -8/3, -2
Put on number line
-8/3         -2          2           4/3

10. 3x2 + 16x + 20 = 0, 3y2 + 8y + 4 = 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
D) If X ≤ Y
Explanation:

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

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