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We are providing the most important **Quadratic Equations (Inequalities) for SBI PO 2019, SBI Clerk 2019** and all **other competitive bank and insurance exams**. These questions have very high chances to be asked in **SBI PO 2019, SBI Clerk 2019.
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Directions:1-10) **In each of these questions two equations (I) and (II) are given. You have to solve both the equations and give answer.**

1.

- x^2 – 26x + 168 = 0
- y^2 – 25y + 156 = 0

2.

- 6x – 5y = -47
- 5x + 3y = 11

3.

I.2.3x – 20.01 = 0

II.2.9y – x = 0

4.

- x = √1764
- y^2 = 1764

5.

- x^2 – 13x + 42 = 0
- y^2 + y – 42 = 0

6.

- 77X
^{2 }+ 58X +8=0 - 56Y
^{2}+29Y +3=0

7.

- 43X
^{2 }– 90X +8=0 - 56Y
^{2}-36Y +4=0

8.

I. 34X^{2 }– 140X +16=0

II. 24Y^{2}-55Y+26=0

9.

- 28X
^{2 }– 75X +17=0 - 36Y
^{2}-71Y +14=0

10.

- 19X
^{2 }– 84X +32=0 - 17Y
^{2}-75Y +28=0

**Check your Answers below:**

Directions:1-10)

**In each of these questions two equations (I) and (II) are given. You have to solve both the equations and give answer.**##### 1. Question

- x^2 – 26x + 168 = 0
- y^2 – 25y + 156 = 0

Ans:5- x^2 – 26x + 168 = 0

X^2 – 12x – 14x + 168 = 0

x (x – 12) – 14(x – 12) = 0

(x – 12) (x – 14) = 0

x = 12, 14

II.y^2 – 25y + 156 = 0

y^2 – 13y – 12y + 156 = 0

y(y – 13) – 12(y – 13) = 0

(y – 12) (y – 13) = 0

y = 12, 13

**Hence, no relation can be established between x and y**##### 2. Question

- 6x – 5y = -47
- 5x + 3y = 11

Ans:3

Equation (I) × 3 = 18x – 15y = -141Equation (II) × 5 = 25x + 15y = 55

43x = -86

X = – 86/43 = 2

From II, we have,

5x + 3y = 11

3y = 11 – 5x

3y = 11 + 10

3y = 21

y = 7

**Hence x < y**##### 3. Question

I.2.3x – 20.01 = 0

II.2.9y – x = 0

Ans:1

I.2.3x – 20.01 = 0X = 20.01 / 2.3 = 8.7

II.2.9y – x = 0

or, x = 2.9y

y = 8.7 /2.9 = 3

**Hence x > y**##### 4. Question

- x = √1764
- y^2 = 1764

Ans:2

I.x = 1764x = 42

II.y^2 = 1764

y = + 42

**Hence x ≥ y**##### 5. Question

- x^2 – 13x + 42 = 0
- y^2 + y – 42 = 0

Ans:2

I.x^2 – 13x + 42 = 0x^2 – 6x – 7x + 42 = 0

x(x – 6) – 7(x – 6) = 0

(x – 6) (x – 7) = 0

x = 6, 7

II.y^2 + y – 42 = 0

y^2 + 7y – 6x – 42 = 0

y(y + 7) – 6(y + 7) = 0

(y – 6)(y + 7) = 0

y = 6, – 7

**Hence x ≥ y**##### 6. Question

- 77X
^{2 }+ 58X +8=0 - 56Y
^{2}+29Y +3=0

Ans:5- 77X
^{2 }+ 58X +8=0 - 56Y
^{2}+29Y +3=0

Sol: I. 77X

^{2 }+ 58X +8=0Or, 77X

^{2}+44X+14X+8=0Or, 11X(7X+4)+2(7X+4)=0

Or, (11X+2)(7X+4)=0

Or, X= (-2)/11 , (-4)/7

- 56Y
^{2}+29Y +3=0

Or, 56Y

^{2}+8Y+21Y+3=0Or, 8Y(7Y+1)+3(7Y+1)=0

Or, (8Y+3)(7Y+1)=0

Or, Y= (-3)/8 , (-1)/7

Hence, on relationship between x and y cannot be established

- 77X
##### 7. Question

- 43X
^{2 }– 90X +8=0 - 56Y
^{2}-36Y +4=0

Ans:5- 43X
^{2 }– 90X +8=0 - 56Y
^{2}-36Y +4=0

Sol: I. 43X

^{2 }– 90X +8=0Or, 43X

^{2}-86X-4X+8=0Or, 43X(X-2)-4(X-2)=0

Or, (43X-4)(X-2)=0

Or, X= 2 , 4/43

- 56Y
^{2}-36Y +4=0

Or, 56Y

^{2}-28Y-8Y+4=0Or, 28Y(2Y-1)-4(2Y-1)=0

Or, (28Y-4)(2Y-1)=0

Or, Y = 4/28, 1/2

Hence, on relationship between x and y cannot be established

- 43X
##### 8. Question

I. 34X

^{2 }– 140X +16=0II. 24Y

^{2}-55Y+26=0Ans:5- 34X
^{2 }– 140X +16=0 - 24Y
^{2}-55Y+26=0

Sol: I. 34X

^{2 }– 140X +16=0Or, 34X

^{2}-136X-4X+16=0Or, 34X(X-4)-4(X-4)=0

Or, (34X-4)(X-4)=0

Or, X = 4, 4/34

- 24Y
^{2}-55Y+26=0

Or, 24Y

^{2}-16Y-39Y+26=0Or, 8Y(3Y-2)-13(3Y-2)=0

Or, (8Y-13)(3Y-2)=0

Or, Y=2/3, 13/8

Hence, on relationship between x and y cannot be established

- 34X
##### 9. Question

- 28X
^{2 }– 75X +17=0 - 36Y
^{2}-71Y +14=0

Ans:5- 28X
^{2 }– 75X +17=0 - 36Y
^{2}-71Y +14=0

Sol: I. 28X

^{2 }– 75X +17=0Or, 28X

^{2}-7X-68X+17=0Or, 7X(4X-1)-17(4X-1)=0

Or, (7X-17)(4X-1)=0

Or, X= 17/7, 1/4

- 36Y
^{2}-71Y +14=0

Or, 36Y

^{2}-8Y-63Y+14=0Or, 4Y(9Y-2)-7(9Y-2)=0

Or, (4Y-7)(9Y-2)=0

Or, Y = 7/4 , 2/9

Hence, on relationship between x and y cannot be established

- 28X
##### 10. Question

- 19X
^{2 }– 84X +32=0 - 17Y
^{2}-75Y +28=0

Ans:5- 19X
^{2 }– 84X +32=0 - 17Y
^{2}-75Y +28=0

Sol: I. 19X

^{2 }– 84X +32=0Or, 19X

^{2}-76X-8X+32=0Or, 19X(X-4)-8(X-4)=0

Or, (19X-8)(X-4)=0

Or, X= 4 , 8/19

- 17Y
^{2}-75Y +28=0

Or, 17Y

^{2}– 68Y-7Y+28=0Or, 17Y(Y-4)-7(Y-4)=0

Or, (17Y-7)(Y-4)=0

Or, Y= 4 ,7/17

Cannot be determined

- 19X