# Set-22 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.
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Directions:1-5) In the following question, two equations I and II are given. Solve both the equations carefully & answer the questions given below:

1.
X2 -6 √3 X -48 =0
Y2 – √2y -24 =0

2.
X2+5 √3 X -42 =0
Y2 – 8 √2 y +30 = 0

3.
X2 +4 √10 x+40 =0
4 √3 Y2 -5y -2 √3 =0

4.
X2– √2 x -24 =0
Y2 – 8  √3 y +48 =0

5.
2X2 – (4+√13) x +2 √13 =0
10y2 – (18+5 √13) y +9 √13 =0

Directions:6-10) In the following question, two equations I and II are given. Solve both the equations carefully & answer the questions given below:

6.
3x+5y =69
9x+4y =108

7.
63x -194x1/2+143 =0
99y-255y1/2+150=0

8.
12x2 + 11 x + 12 = 10x2+22x
13y2 – 18y + 3 = 9y2 – 10y

9.
16x2 – 40x – 39 = 0
12y2 – 113y + 255 = 0

10.
(X1/4 )2/625 =169/X3/2
Y4/3* Y2/3*2786 =7*Y3

Check your Answers below:

1. Directions:1-5) In the following question, two equations I and II are given. Solve both the equations carefully & answer the questions given below:

##### 1. Question

X2 -6 √3 X -48 =0
Y2 – √2y -24 =0

Ans:3
X2 -6 3 X -48 =0X(x -8 3) +2 3 (x -8 3) =0

(X -8 3) (x + 2 3) =0

X =8 3, – 2 3

Y2 2y -24 =0

Y2 – 4 2y +3 2y -24 =0

Y = 4 2, – 3 2

Relationship cannot be determined

2. ##### 2. Question

X2+5 √3 X -42 =0
Y2 – 8 √2 y +30 = 0

Ans:2
X2+5 3 X -42 =0(X +7 3) (X – 23) =0

X = -7 3, 2 3

Y2 – 8 2y +30 = 0

Y = 5 2 , 3 2

x < y

3. ##### 3. Question

X2 +4 √10 x+40 =0
4 √3 Y2 -5y -2 √3 =0

Ans:2
X2 +4 √10 x + 40=0(X +2 10) (X +2 10) =0

X= – 2 10, – 2 10

4 3 Y2 -5y -2 3 =0

Y = +8 /43, -3 / 4 3

x < y

4. ##### 4. Question

X2– √2 x -24 =0
Y2 – 8  √3 y +48 =0

Ans:2
X2 2X -24 =0X2 – 4 2X +3 2X -24 =0

X = 4 2 ,  -3 2

Y2 – 8 3 y +48 =0

(Y -4 3 ) (Y -4 3 ) =0

Y =4 3   , 4 3

x < y

5. ##### 5. Question

2X2 – (4+√13) x +2 √13 =0
10y2 – (18+5 √13) y +9 √13 =0

Ans:3
2X2 – (4+13)x +2 13 =0X = 4 /2, 13/2

X=2, 1.8

10y2 – (18+5 13)y +9 13 =0

Y = 18/10, 5 13 /10

Y =1.8, 1.8

x ≥ y

Directions:6-10) In the following question, two equations I and II are given. Solve both the equations carefully & answer the questions given below:

##### 6. Question

3x+5y =69
9x+4y =108

Ans:2
9x+4y =108 ——– (1)3x+5y =69 ——— (2­)

à(2)*3

9x+15y = 207

9x+4y =108

11y =99

Y=9

9x +36 =108

9x=72

X=8

x < y

6. ##### 7. Question

63x -194x1/2+143 =0
99y-255y1/2+150=0

Ans:5

1. 63x -194 x1/2+143 = 0

Or 63x -117 x ½ -77 x ½ +143 = 0

Or (7 x1/2 -13) (9 x1/2 -11) = 0

x =169/ 49,121/81

1. 99y – 255 y ½ +150 = 0

or 99y – 165 y 1/2 – 90 y 1/2 +150 = 0

or (11y1/2 – 10)(9y1/2 -15) = 0

y = 100/121, 225/81

7. ##### 8. Question

12x2 + 11 x + 12 = 10x2+22x
13y2 – 18y + 3 = 9y2 – 10y

Ans:3
12x2 + 11 x + 12 = 10x2+22x2x2 -11x +12 =0

X =8/2, 3/2 = 4, 1.5

13y2 – 18y + 3 = 9y2 – 10y

4y2 -8y +3 =0

Y = 6/4, 2/4 =1.5, 0.5

X≥ y

8. ##### 9. Question

16x2 – 40x – 39 = 0
12y2 – 113y + 255 = 0

Ans:2
16x2 – 40x – 39 = 0or 16x2 – 52x + 12x – 39 = 0

or (4x- 13) (4x + 3)

x= 13/4, – ¾

12y2 – 113y + 255 = 0

or 12y2 – 45y – 68y + 255 = 0

or (4y – 15) (3y – 17) = 0

y =15/4, 17/3

x < y

9. ##### 10. Question

(X1/4 )2/625 =169/X3/2
Y4/3* Y2/3*2786 =7*Y3

Ans:2
X1/2 /625 =169/X3/2X2 = 625*169

X=  ± (25*13) = ±325

Y6/3*2786 =7*y3

Y =2786/7 =398

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