# Set-13 Quadratic Equations (Inequalities) For SBI PO and SBI Clerk 2019 | Must Go Through These Questions

Dear Aspirants,
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.

Directions:1-5) In the following questions, two equations numbered are given in variables a and b. You have to solve both the equations and find out the relationship between a and b. Then give answer accordingly-

1.

I.3a2 – 8a – 28 = 0
II.3b2 – 44b + 140 = 0

2.

I.2a2 – 27a + 81 = 0
II.3b2 – 50b + 168 = 0

3.

I.2a2 – 27a + 81 = 0
II.3b2 – 50b + 168 = 0

4.

I.3a2 – 14a – 24 = 0
II.3b2 + 32b + 64 = 0

5.

I.4a2 + a – 18 = 0
II.4b2 – 11b – 45 = 0

Directions:6-10) In each of these questions, two equations numbered I and II with variables x and y are given. You have to solve both the equations to find the relation between x and y.

6.

I. 5x2 – 176x – 333 = 0

II. 49y2 – 84y + 36 = 0

7.

I. x2 + 13√2x + 84 = 0

II. 12y2 – 20y + 8 = 0

8.

I. 20x2 – 108x + 144 = 0

II. y2 – 26y + 168 = 0

9.

I. x2 – 32x + 252 = 0

II. 25y2 – 90y + 72 = 0

10.

I. x2 – 56x + 783 = 0

II. 12y2 + 82y + 140 = 0

• Directions:1-5) In the following questions, two equations numbered are given in variables a and b. You have to solve both the equations and find out the relationship between a and b. Then give answer accordingly-

##### 1. Question

I.3a2 – 8a – 28 = 0
II.3b2 – 44b + 140 = 0

Ans:4
3a2 – 8a – 28 = 0
3a2 + 6a – 14a – 28 = 0
Gives a = -2, 14/3
3b2 – 44b + 140 = 0
3b2 – 30b -14b + 140 = 0
Gives b = 14/3, 10
a ≤ b

• ##### 2. Question

I.2a2 – 27a + 81 = 0
II.3b2 – 50b + 168 = 0

Ans:4
2a2 – 27a + 81 = 0
2a2 – 18a – 9a + 81 = 0
Gives a = 9/2, 9
3b2 – 50b + 168 = 0
3b2 – 36b – 14b + 168 = 0
Gives b = 14/3, 12
Cannot be determined

• ##### 3. Question

I.2a2 – 27a + 81 = 0
II.3b2 – 50b + 168 = 0

Ans:5
2a2 – 27a + 81 = 0
2a2 – 18a – 9a + 81 = 0
Gives a = 9/2, 9
3b2 – 50b + 168 = 0
3b2 – 36b – 14b + 168 = 0
Gives b = 14/3, 12
Cannot be determined

• ##### 4. Question

I.3a2 – 14a – 24 = 0
II.3b2 + 32b + 64 = 0

Ans:1
3a2 – 14a – 24 = 0
3a2 – 18a + 4a – 24 = 0
Gives a = -4/3, 6
3b2 + 32b + 64 = 0
3b2 + 24b + 8b + 64 = 0
Gives b= -8, -8/3
a > b

• ##### 5. Question

I.4a2 + a – 18 = 0
II.4b2 – 11b – 45 = 0

Ans:5
4a2 + a – 18 = 0
4a2 – 8a + 9a – 18 = 0
Gives a = -9/4, 2
4b2 – 11b – 45 = 0
4b2 – 20b + 9b – 45 = 0
Gives b= -9/4, 5

Cannot be determined

Directions:6-10) In each of these questions, two equations numbered I and II with variables x and y are given. You have to solve both the equations to find the relation between x and y.

##### 6. Question

I. 5x2 – 176x – 333 = 0

II. 49y2 – 84y + 36 = 0

Ans:5
I. 5x2 – 176x – 333 = 0

=> (x – 37)(5x + 9) = 0

=> x = 37, -9/5

II. 49y2 – 84y + 36 = 0

=> (7y – 6)2 = 0

=>7y – 6 = 0

=> y = 6/7

Hence, relationship between x and y cannot be determined.

• ##### 7. Question

I. x2 + 13√2x + 84 = 0

II. 12y2 – 20y + 8 = 0

Ans:3
I. x2 + 13√2x + 84 = 0

=> (x + 6√2)(x + 7√2) = 0

=> x = -6√2, -7√2

II. 12y2 – 20y + 8 = 0

=> 3y2 – 5y + 2 = 0

=> (3y – 2)(y – 1) = 0

=> y = 2/3, 1

Hence, x < y

• ##### 8. Question

I. 20x2 – 108x + 144 = 0

II. y2 – 26y + 168 = 0

Ans:3
I. 20x2 – 108x + 144 = 0

=>5x2 – 27x + 36 = 0

=> (5x – 12)(x – 3) = 0

=> x = 12/5, 3

II. y2 – 26y + 168 = 0

=> (y – 12)(y – 14) = 0

=> y = 12, 14

Hence, x < y

• ##### 9. Question

I. x2 – 32x + 252 = 0

II. 25y2 – 90y + 72 = 0

Ans:1
I. x2 – 32x + 252 = 0

=> (x – 18)(x – 14) = 0

=> x = 18, 14

II. 25y2 – 90y + 72 = 0

=> (5y – 12)(5y – 6) = 0

=> y = 12/5, 6/5

Hence, x > y

• ##### 10. Question

I. x2 – 56x + 783 = 0

II. 12y2 + 82y + 140 = 0

Ans:1
I. x2 – 56x + 783 = 0

=> (x – 29)(x – 27) = 0

=> x = 29, 27

II. 12y2 + 82y + 140 = 0

=> 6y2 + 41y + 70 = 0

=> (2y + 7)(3y + 10) = 0

=> y = -7/2, -10/3

Hence, x > y

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