Quadratic Equation Bank PO

**Directions: In the following questions, two equations numbered are given in variables x and y. You have to solve both the equations and find out the relationship between x and y. Then give answer accordingly-**

** I. 20x**^{2} – 31x + 12 = 0,

II. 6y^{2} – 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

View Answer

** A) If x > y**

Solution:

20x^{2} – 31x + 12 = 0

20x^{2} – 16x – 15x + 12 = 0

So x = 3/4, 4/5

6y^{2} – 7y + 2 = 0

6y^{2} – 3y – 4y + 2 = 0

So y = 1/2, 2/3

Put on number line

1/2… 2/3… 3/4… 4/5

** I. 3x**^{2} + 22 x + 24 = 0,

II. 3y^{2} – 10y + 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

View Answer

** B) If x < y**

Solution:

3x^{2} + 22 x + 24 = 0

3x^{2} + 18x + 4x + 24 = 0

So x = -4/3, -6

3y^{2} – 10y + 3 = 0

3y^{2} – 9y – y + 3 = 0

So y = 1/3, 3

Put on number line

-6… -4/3… 1/3… 3

** I. 6x**^{2} – x – 2 = 0,

II. 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

View Answer

** E) If x = y or relation cannot be established**

Solution:

6x^{2} – x – 2 = 0

6x^{2} + 3x – 4x – 2 = 0

So x = -1/2, 2/3

5y^{2} – 18y + 9 = 0

5y^{2} – 15y – 3y + 9 = 0

So y = 3/5, 3

Put on number line

-1/2 …. 3/5 ….2/3 …. 3

** I. x**^{2} – x – 6 = 0,

II. 5y^{2} – 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

View Answer

** E) If x = y or relation cannot be established**

Solution:

x^{2} – x – 6 = 0

x^{2} – 2x + 3x – 6 = 0

So x = -3, 2

5y^{2} – 7y – 6 = 0

5y^{2} – 10y + 3y – 6 = 0

So y = -3/5, 2

Put on number line

-3 …. -3/5….. 2

** I. 3x**^{2} – 10x + 8 = 0,

II. 3y^{2} + 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

View Answer

** C) If x ≥ y**

Solution:

3x^{2} – 10x + 8 = 0

3x^{2} – 6x – 4x + 8 = 0

So x = 2, 4/3

3y^{2} + 8y – 16 = 0

3y^{2} + 12y – 4y – 16 = 0

So y = -4, 4/3

Put on number line

-4 …. 4/3…. 2

** I. 2x**^{2} + 17x + 30 = 0,

II. 2y^{2} + 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

View Answer

** E) If x = y or cannot be established**

Solution:

2x^{2} + 17x + 30 = 0

2x^{2} + 12x + 5x + 30 = 0

So x = -6, -5/2

2y^{2} + 13y + 18 = 0

2y^{2} + 4y + 9y + 18 = 0

So y = -9/2, -2

Put on number line

-6 … -9/2 …. -5/2 …. -2

** I. 3x**^{2} + 16x + 20 = 0,

II. 3y^{2} + 8y + 4 = 0

A) x > y

B) x < y

C) x ≥ y

D) x ≤ y

E) x = y or relationship cannot be determined

View Answer

** D) If x ≤ y**

Solution:

3x^{2} + 16x + 20 = 0

3x^{2} + 6x + 10x + 20 = 0

So x = -10/3, -2

3y^{2} + 8y + 4 = 0

3y^{2} + 6y + 2y + 4 = 0

So y = -2, -2/3

put on number line

-10/3…. -2…. -2/3

** I. x**^{2} + x – 20 = 0,

II. 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

View Answer

** E) If x = y or relation cannot be established**

Solution:

x^{2} + x – 20 = 0

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

So x = -5, 4

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

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

So y = -5, -3/2

Put on number line

-5…. -3/2…. 4

** I. 5x**^{2} – 7x – 6 = 0,

II. 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

View Answer

** C) If x ≥ y**

Solution:

5x^{2} – 7x – 6 = 0

5x^{2} – 10x + 3x – 6 = 0

So x = -3/5, 2

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

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

So y = -4, -3/5

Put on number line

-4….. -3/5…. 2

** I. 2x**^{2} – 9x + 4 = 0,

II. 2y^{2} + 7y – 4 = 0

A) x > y

B) x < y

C) x ≥ y

D) x ≤ y

E) x = y or relationship cannot be determined

View Answer

** C) If x ≥ y**

Solution:

2x^{2} – 9x + 4 = 0

2x^{2} – 8x – x + 4 = 0

So x = 4 , 1/2

2y^{2} + 7y – 4 = 0

2y^{2} + 8y – y – 4 = 0

So y = -4, 1/2

Put on number line

-4……. 1/2…… 4

#### Click here to go to Quantitative Aptitude Section.

*Related*