Dear Readers,

Today we are presenting you Quant Mania on Quadratic Inequality which is very important for your upcoming LIC AAO and other exams. You may expect same questions in your upcoming exams. Try to solve it.

## Quadratic Inequality

**Directions (Q. 1-5): In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer.**

**1. I. x**

^{2}– 25 = 0, II. y^{2 }– 3y - 18 = 0
a) if x > y

b) if x ≥ y

c) if x < y

d) if x ≤ y

e) if x = y or no relation can be established between x and y.

**2. I. 2x**

^{2}– 3x + 1 = 0, II. 2y^{2 }- 9y + 9 = 0
a) if x > y

b) if x ≥ y

c) if x < y

d) if x ≤ y

e) if x = y or no relation can be established between x and y.

**3. I. x**

^{2}= 4y, II. y = (729)^{1/3}

a) if x > y

b) if x ≥ y

c) if x < y

d) if x ≤ y

e) if x = y or no relation can be established between x and y.

**4. x**

^{2}– 5x + 6 = 0, II. y^{2 }- 3y + 2 = 0
a) if x > y

b) if x ≥ y

c) if x < y

d) if x ≤ y

e) if x = y or no relation can be established between x and y.

**5. I. 3x**

^{2 }– 19x + 20=0, II. (3y – 4) (y – 5) = 0
a) if x > y

b) if x ≥ y

c) if x < y

d) if x ≤ y

e) if x = y or no relation can be established between x and y.

### Answers with Solution

1. e;I. x2 – 25 = 0

or, x2 = 25

or, x = ± 5

II. y2 – 3y - 18 = 0

or, y2 - 6y + 3y - 18= 0

or, y(y - 6) + 3(y - 6) = 0

or, (y - 6) (y + 3) = 0

or, y = 6, -3

Hence, no relation can be established.

2. c;

I. 2x2 – 3x + 1 = 0

or, 2x2 – 2x - 1x + 1 = 0

or, 2x(x – 1) - 1(x - 1) = 0

or, (2x – 1) (x - 1) = 0

x = ½, 1

II. 2y2 - 9y + 9 = 0

or, 2y2 - 6y - 3y + 9 = 0

or, 2y(y - 3) - 3(y - 3) = 0

or, (2y - 3) (y - 3) = 0

y = 3/2, 3

Hence, x < y

3. c;

II. y = (729)1/3

y = 9

I. x2 = 4y

or, x2 = 4 * 9 = 36

or, x = ±6

Hence,

I. x2 – 5x + 6 = 0

or, x2 – 3x - 2x + 6 = 0

or. x(x - 3) - 2(x – 3) = 0

or, (x - 3) (x - 2) = 0

x = 3, 2

II. y2 - 3y + 2 = 0

or, y2 - 2y - y + 2 = 0

or, y(y - 2) - 1(y - 2) = 0

or, (y - 2) (y - 1) = 0

y = 1, 2

Hence, x ≥ y

5. e;

I. 3x2 – 19x + 20 = 0,

or, 3x2 – 15x – 4x+ 20 = 0

or, 3x(x – 5) – 4(x – 5) = 0

or, (3x – 4) (x – 5) = 0

x = 4/3, 5

II. (3y – 4) (y – 5) = 0

y = 4/3, 5

Hence, x = y

*Thanks.*

*Smart Prep Kit by Ramandeep Singh - Get here*####
*Bank Exams Today Notes*

*Bank Exams Today Notes*

## 0 comments:

## Post a Comment

Thanks for commenting. It's very difficult to answer every query here, it's better to post your query on IBPSToday.com