Set-7 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:1-10) In each of the following questions two equations and are given. You have to solve both the equations and give answer

1.

1. 9P2– 9P + 2 = 0
2. 18Q2+ 3Q = 1

2.

1. I. P2+ 13P + 42 = 0
2. 2Q2+ 22Q + 60 = 0

3.

1. I. 6P + 7Q = 45
2. 2P + 3Q = 17

4.

1. I. 3P2+ 192 = – 48P
2. Q2+ 16Q + 64 = 0

5.

I. 15P2– 8P + 1 = 0

II. 45Q2+ 21Q = 6

6.

I. X – 8/√X=0
II. √Y- √7/√Y=0

7.

I. 8X2+78X+169=0

II. 5Y2+ 14Y+8=0

8.

I. 12X2-5X-25=0

II. 12Y2+17Y-40=0

9.

I. 15X+13Y=221

II. 4Y+2X=51

10.

6X2+34=29X

8Y2+3Y=38

1. Directions:1-10) In each of the following questions two equations and are given. You have to solve both the equations and give answer

1. Question
1. 9P2– 9P + 2 = 0
2. 18Q2+ 3Q = 1
Ans:5
9P2 – 9P + 2 = 0

Or,  9P2 – 6P – 3P + 2 = 0

Or, (3P – 1)(3P – 2) = 0

P = (1 / 3), (2 / 3)

Ⅱ. 18Q2 + 3Q – 1 = 0

Or, 18Q2 + 6Q – 3Q – 1 = 0

Or, (6Q – 1)(3Q + 1) = 0

Q = – (1 / 3), (1 / 6)

Hence, P > Q

2. 2. Question
1. I. P2+ 13P + 42 = 0
2. 2Q2+ 22Q + 60 = 0
Ans:2
P2 + 13P + 42 = 0

Or,  P2 + 7P + 6P + 42 = 0

Or, (P + 7)(P + 6) = 0

∴ P = -7, -6

Ⅱ. 2Q2 + 22Q + 60 = 0

Or, Q2 + 11Q + 30  = 0

Or, (Q + 5)(Q + 6) = 0

∴ Q = -5, -6

Hence , Q ≥  P

3. 3. Question
1. I. 6P + 7Q = 45
2. 2P + 3Q = 17
Ans:5
P = 4 and Q = 3

Hence P > Q

4. 4. Question
1. I. 3P2+ 192 = – 48P
2. Q2+ 16Q + 64 = 0
Ans:4
3P2 + 48P + 192 = 0

Or,  P2 + 16P + 64 = 0

Or, (P + 8)2 = 0

∴ P = -8

Ⅱ. Q2 + 16Q + 64 = 0

Or, (Q + 8)2 = 0

∴ Q = -8

Hence , P = Q

5. 5. Question

I. 15P2– 8P + 1 = 0

II. 45Q2+ 21Q = 6

Ans:3
15P2 – 8P + 1 = 0

Or,  15P2 – 3P – 5P + 1 = 0

Or, (3P – 1)(5P – 1) = 0

∴ P = (1 / 3), (1 / 5)

Ⅱ. 45Q2 + 21Q – 6 = 0

15Q2 + 7Q – 2 = 0

Or, 15Q2 + 10Q – 3Q – 2 = 0

Or, (5Q – 1)(3Q + 2) = 0

∴ Q =  (1 / 5), – (2 / 3)

Hence, P ≥ Q

6. 6. Question

I. X – 8/√X=0

II. √Y- √7/√Y=0

Ans:1
I. X – 8/√X=0

Or, x3/2= 8

Or, X = 4

II. √Y- √7/√Y=0

Or, Y = √7

Y =  2.6

Hence X > Y

7. 7. Question

I. 8X2+78X+169=0

II. 5Y2+ 14Y+8=0

Ans:3
I. 8X2+78X+169=0

Or, 8X2+52X+26X+169=0

Or, 4X(2X+13)+ 13(2X+13)=0

Or, (4X+13)(2X+13)=0

X= (-13)/4,(-13)/2

II.5Y2+ 14Y+8=0

Or, 5Y2+10Y+4Y+8=0

Or, 5Y(Y+2)+4(Y+2)=0

Or, (5Y+4)(Y+2)=0

Y= -2 , (-4)/5

Hence X< Y

8. 8. Question

I. 12X2-5X-25=0

II. 12Y2+17Y-40=0

Ans:5
I. 12X2-5X-25=0

Or, 12X2+15X-20X-25=0

Or, 3X(4X+5)-5(4X+5)=0

Or, (3X-5)(4X+5)=0

X = 5/3,(-5)/4

II. 12Y2+17Y-40=0

Or, 12Y2-15Y+32Y-40=0

Or,  3Y(4Y-5)+8(4Y-5)=0

Or, (3Y+8)(4Y-5)=0

Y = 5/4,(-8)/3

Hence the relationship between x and y cannot be established

9. 9. Question

I. 15X+13Y=221

II. 4Y+2X=51

Ans:3
15X+13Y=221 … (i) ×4

2X+4Y=51 … (ii) × 13

60X + 52Y = 884 …. iii

26X + 52Y = 663 ….iv

After solving (iii) and (iv), we have

34X = 221

Or, X = 6.5

Putting the value of X in (i), we get

Or, 97.5 + 13Y= 221

Or, 13Y=123.5

Y= 9.5

Hence X< Y

10. 10. Question

6X2+34=29X

8Y2+3Y=38

Ans:2
. 6X2 -29X+34=0

Or, 6X2-12X-17X+34=0

Or, 6X(X-2)-17(X-2)=0

Or, (6X-17)(X-2)=0

X= 2, 17/6

II. 8Y2+3Y=38

Or,  8Y2+3Y-38=0

Or, 8Y2-16Y+19Y-38=0

Or,  8Y(Y-2)+19(Y-2)=0

Or, (8Y+19)(Y-2)=0

Y= 2, (-19)/8

Hence X ≥ Y

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