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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 the following questions two equations Ⅰ and Ⅱ are given. You have to solve both the equations and give answer
1.
- 9P2– 9P + 2 = 0
- 18Q2+ 3Q = 1
2.
- I. P2+ 13P + 42 = 0
- 2Q2+ 22Q + 60 = 0
3.
- I. 6P + 7Q = 45
- 2P + 3Q = 17
4.
- I. 3P2+ 192 = – 48P
- 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
Check your Answers below:
Directions:1-10) In each of the following questions two equations Ⅰ and Ⅱ are given. You have to solve both the equations and give answer
1. Question
- 9P2– 9P + 2 = 0
- 18Q2+ 3Q = 1
Ans:5
9P2 – 9P + 2 = 0Or, 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. Question
- I. P2+ 13P + 42 = 0
- 2Q2+ 22Q + 60 = 0
Ans:2
Ⅰ. P2 + 13P + 42 = 0Or, 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. Question
- I. 6P + 7Q = 45
- 2P + 3Q = 17
Ans:5
P = 4 and Q = 3Hence P > Q
4. Question
- I. 3P2+ 192 = – 48P
- Q2+ 16Q + 64 = 0
Ans:4
Ⅰ. 3P2 + 48P + 192 = 0Or, 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. Question
I. 15P2– 8P + 1 = 0
II. 45Q2+ 21Q = 6
Ans:3
Ⅰ. 15P2 – 8P + 1 = 0Or, 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. Question
I. X – 8/√X=0
II. √Y- √7/√Y=0
Ans:1
I. X – 8/√X=0Or, x3/2= 8
Or, X = 4
II. √Y- √7/√Y=0
Or, Y = √7
Y = 2.6
Hence X > Y
7. Question
I. 8X2+78X+169=0
II. 5Y2+ 14Y+8=0
Ans:3
I. 8X2+78X+169=0Or, 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. Question
I. 12X2-5X-25=0
II. 12Y2+17Y-40=0
Ans:5
I. 12X2-5X-25=0Or, 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. Question
I. 15X+13Y=221
II. 4Y+2X=51
Ans:3
15X+13Y=221 … (i) ×42X+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. Question
6X2+34=29X
8Y2+3Y=38
Ans:2
. 6X2 -29X+34=0Or, 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