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 !!!

Follow the link **To solve Quadratic Equations with the help of Number Line**

**x**^{2}– 18x + 72= 0, 5y^{2}– 18y + 9 = 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:

x^{2}– 18x + 72= 0

(x-12)(x-6) = 0

Gives x = 6, 12

5y^{2}– 18y + 9 = 0

5y^{2}– 15y – 3y + 9 = 0

Gives y = 3/5, 3

Put on number line

3/5 3 6 12**x**^{2}= 4, 3y^{2}– 4y – 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**E) If X=Y or cannot be established**

Explanation:

x^{2}= 4

Gives x = 2 , -2

3y^{2}– 4y – 4 = 0

3y^{2}– 6y + 2y – 4 = 0

Gives y = -2/3, 2

Put on number line

-2 -2/3 2

When y = 2, y ≥ x

When y = -2/3, y > x(-2) and y < x(2)

So no relation**6x**^{2}– 5x – 6 = 0, 2y^{2}– 13y + 20 = 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:

6x^{2}– 5x – 6 = 0

6x^{2}– 9x + 4x – 6 = 0

Gives x = -2/3, 3/2

2y^{2}– 13y + 20 = 0

2y^{2}– 8y – 5y +20 = 0

Gives y = 4, 5/2

Put on number line

-2/3 3/2 5/2 4**2x**^{2}– 5x = 0, 2y^{2}+ 7y – 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**E) If X=Y or cannot be established**

Explanation:

2x^{2}– 5x = 0

x(2x-5) = 0

Gives x = 0, 5/2

3y^{2}– 7y – 6 = 0

3y^{2}– 9y + 2y – 6 = 0

Gives y = -2/3, 3

Put on number line

-2/3 0 5/2 3**2x**^{2}+ 5x + 2= 0, 2y^{2}+ 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**A) If X > Y**

Explanation:

2x^{2}+ 5x + 2= 0

2x^{2}+ 4x + x + 2= 0

Gives x = -1/2, -2

2y^{2}+ 19y + 45 = 0

2y^{2}+ 10y + 9y + 45 = 0

Gives y= -10/2, -9/2

Put on number line

-10/2 -9/2 -2 -1/2**x**^{2}+ x – 20 = 0, 2y^{2}+ 13y + 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**E) If X = Y or relation cannot be established**

Explanation:

x^{2}+ x – 20 = 0

(x+5)(x-4) = 0

Gives x = -5, 4

2y^{2}+ 13y + 15 = 0

2y^{2}+ 10y + 3y + 15 = 0

Gives y = -5, -3/2

Put on number line

-5 -3/2 4**5x**^{2}– 7x – 6 = 0, 5y^{2}+ 23y + 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**C) If X ≥ Y**

Explanation:

5x^{2}– 7x – 6 = 0

5x^{2}– 10x + 3x – 6 = 0

Gives x = -3/5, 2

5y^{2}+ 23y + 12 = 0

5y^{2}+ 20y + 3y + 12 = 0

Gives y = -4, -3/5

Put on number line

-4 -3/5 2**3x**^{2}+ 8x + 5 = 0, 2y^{2}+ y – 1 = 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:

3x^{2}+ 8x + 5 = 0

3x^{2}+ 3x + 5x + 5 = 0

Gives x = -1, -5/3

2y^{2}+ y – 1 = 0

2y^{2}+ 2y – y -1 = 0

Gives y = -1, 1/2

put on number line

-5/3 -1 1/2**2x + 5y = 23.5, 5x+ 2y = 22**

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:

Solve the equations, x = 3, y = 3.5**2x**^{2}– 9x + 10 = 0, 2y^{2}+ 7y – 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**A) If X > Y**

Explanation:

2x^{2}– 9x + 10 = 0

2x^{2}– 9x – 5x + 10 = 0

Gives x = 2, 5/2

2y^{2}+ 7y – 4 = 0

2y^{2}+ 8y – y – 4 = 0

Gives y = -4, 1/2

put on number line

-4 1/2 2 5/2

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