Dear Readers,

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.

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.

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.

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.

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.

I. x

or, x

or. x(x - 5) + 3(x – 5) = 0

or, (x – 5) (x + 3) = 0

x = 5, -3

II. y

or, y

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

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

y = -3, -2

I. x

or, x

or, x(x – 4) + 3(x - 4) = 0

or, (x – 4) (x + 3) = 0

x = 4, -3

II. y

or, y

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

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

y = 1, 2

I. x - √169 = 0

or, x = √169

or, x = 13

II. y2 – 169 = 0

or, y2 – 169 = 0

or, y2 = 169

or, y = ± 13

Hence, x ≥ y

I. x

or, x

or, x

or, x = ± 12

II. y - √256 = 0

or, y = √256

or, y = 16

I. x

or, x

or, x = ± 5

II. y

or, y

or, y(y – 5)– 4(y - 5) = 0

or, (y – 5) (y – 4) = 0

or, y = 5, 4

Today we are presenting you Quant Mania on Quadratic Inequality which is very important for your upcoming LIC AAO, Syndicate Bank PO, SIDBI Officers Scale Grade A and other exams. You may expect same questions in your upcoming exams. Try to solve it.

## Quant Mania: 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}– 2x - 15 = 0, II. y^{2 }+ 5y + 6 = 0b) 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. x**

^{2}– x – 12 = 0, II. y^{2 }- 3y + 2 = 0b) 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 - √169 = 0, II.**

**y**

^{2 }**– 169 = 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.

**4. I.**

**x**

^{2}**- 32 =112, II. y - √256 = 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.**

**x**

^{2}**– 25 = 0, II.**

**y**

^{2 }**– 9y + 20 = 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.

### Answer

**1. b;**

I. x

^{2}– 2x - 15 = 0

or, x

^{2}– 5x + 2x - 15 = 0

or. x(x - 5) + 3(x – 5) = 0

or, (x – 5) (x + 3) = 0

x = 5, -3

II. y

^{2 }+ 5y + 6 = 0

or, y

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

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

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

y = -3, -2

**Hence, x ≥ y**

**2. e;**

I. x

^{2}– x – 12 = 0

or, x

^{2}– 4x + 3x – 12 = 0

or, x(x – 4) + 3(x - 4) = 0

or, (x – 4) (x + 3) = 0

x = 4, -3

II. y

^{2 }- 3y + 2 = 0

or, y

^{2 }- 2y - y + 2 = 0

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

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

y = 1, 2

**Hence, no relation can be established.**

**3. b;**

I. x - √169 = 0

or, x = √169

or, x = 13

II. y2 – 169 = 0

or, y2 – 169 = 0

or, y2 = 169

or, y = ± 13

Hence, x ≥ y

**4. c;**

I. x

^{2}- 32 =112

or, x

^{2}= 112 + 32

or, x

^{2}= 144

or, x = ± 12

II. y - √256 = 0

or, y = √256

or, y = 16

**Hence, x < y**

**5. e;**

I. x

^{2}– 25 = 0

or, x

^{2}= 25

or, x = ± 5

II. y

^{2 }– 9y + 20 = 0

or, y

^{2 }– 5y – 4y + 20 = 0

or, y(y – 5)– 4(y - 5) = 0

or, (y – 5) (y – 4) = 0

or, y = 5, 4

**Hence, no relation can be established.**

*Thanks.*
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