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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.
- 77X2 + 58X +8=0
- 56Y2+29Y +3=0
7.
- 43X2 – 90X +8=0
- 56Y2-36Y +4=0
8.
I. 34X2 – 140X +16=0
II. 24Y2-55Y+26=0
9.
- 28X2 – 75X +17=0
- 36Y2-71Y +14=0
10.
- 19X2 – 84X +32=0
- 17Y2-75Y +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
- 77X2 + 58X +8=0
- 56Y2+29Y +3=0
Ans:5- 77X2 + 58X +8=0
- 56Y2+29Y +3=0
Sol: I. 77X2 + 58X +8=0
Or, 77X2+44X+14X+8=0
Or, 11X(7X+4)+2(7X+4)=0
Or, (11X+2)(7X+4)=0
Or, X= (-2)/11 , (-4)/7
- 56Y2+29Y +3=0
Or, 56Y2+8Y+21Y+3=0
Or, 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
7. Question
- 43X2 – 90X +8=0
- 56Y2-36Y +4=0
Ans:5- 43X2 – 90X +8=0
- 56Y2-36Y +4=0
Sol: I. 43X2 – 90X +8=0
Or, 43X2-86X-4X+8=0
Or, 43X(X-2)-4(X-2)=0
Or, (43X-4)(X-2)=0
Or, X= 2 , 4/43
- 56Y2-36Y +4=0
Or, 56Y2-28Y-8Y+4=0
Or, 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
8. Question
I. 34X2 – 140X +16=0
II. 24Y2-55Y+26=0
Ans:5- 34X2 – 140X +16=0
- 24Y2-55Y+26=0
Sol: I. 34X2 – 140X +16=0
Or, 34X2-136X-4X+16=0
Or, 34X(X-4)-4(X-4)=0
Or, (34X-4)(X-4)=0
Or, X = 4, 4/34
- 24Y2-55Y+26=0
Or, 24Y2-16Y-39Y+26=0
Or, 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
9. Question
- 28X2 – 75X +17=0
- 36Y2-71Y +14=0
Ans:5- 28X2 – 75X +17=0
- 36Y2-71Y +14=0
Sol: I. 28X2 – 75X +17=0
Or, 28X2-7X-68X+17=0
Or, 7X(4X-1)-17(4X-1)=0
Or, (7X-17)(4X-1)=0
Or, X= 17/7, 1/4
- 36Y2-71Y +14=0
Or, 36Y2-8Y-63Y+14=0
Or, 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
10. Question
- 19X2 – 84X +32=0
- 17Y2-75Y +28=0
Ans:5- 19X2 – 84X +32=0
- 17Y2-75Y +28=0
Sol: I. 19X2 – 84X +32=0
Or, 19X2-76X-8X+32=0
Or, 19X(X-4)-8(X-4)=0
Or, (19X-8)(X-4)=0
Or, X= 4 , 8/19
- 17Y2-75Y +28=0
Or, 17Y2– 68Y-7Y+28=0
Or, 17Y(Y-4)-7(Y-4)=0
Or, (17Y-7)(Y-4)=0
Or, Y= 4 ,7/17
Cannot be determined
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