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300+ Most Asked Quadratic Equation for Bank Exam

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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

Ans:5
Ⅰ. 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.

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

Ans:2
Ⅰ. 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.

  1. I. 6P + 7Q = 45
  2. 2P + 3Q = 17

Ans:5
P = 4 and Q = 3

Hence P > Q

4.

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

Ans:4
Ⅰ. 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.

I. 15P2– 8P + 1 = 0

II. 45Q2+ 21Q = 6

Ans:3
Ⅰ. 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.

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.

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.

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.

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.
6X2+34=29X

8Y2+3Y=38

Ans:2
I. 6X-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