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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:1-5) 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:
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 =0Ans: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. Question
X2+5 √3 X -42 =0
Y2 – 8 √2 y +30 = 0Ans:2
X2+5 √3 X -42 =0(X +7 √3) (X – 2√3) =0X = -7 √3, 2 √3
Y2 – 8 √2y +30 = 0
Y = 5 √2 , 3 √2
x < y
3. Question
X2 +4 √10 x+40 =0
4 √3 Y2 -5y -2 √3 =0Ans:2
X2 +4 √10 x + 40=0(X +2 √10) (X +2 √10) =0X= – 2 √10, – 2 √10
4 √3 Y2 -5y -2 √3 =0
Y = +8 /4 √3, -3 / 4 √3
x < y
4. Question
X2– √2 x -24 =0
Y2 – 8 √3 y +48 =0Ans:2
X2 – √2X -24 =0X2 – 4 √2X +3 √2X -24 =0X = 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. Question
2X2 – (4+√13) x +2 √13 =0
10y2 – (18+5 √13) y +9 √13 =0Ans:3
2X2 – (4+√13)x +2 √13 =0X = 4 /2, √13/2X=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 =108Ans: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
7. Question
63x -194x1/2+143 =0
99y-255y1/2+150=0Ans:5
- 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
- 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
8. Question
12x2 + 11 x + 12 = 10x2+22x
13y2 – 18y + 3 = 9y2 – 10yAns:3
12x2 + 11 x + 12 = 10x2+22x2x2 -11x +12 =0X =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
9. Question
16x2 – 40x – 39 = 0
12y2 – 113y + 255 = 0Ans:2
16x2 – 40x – 39 = 0or 16x2 – 52x + 12x – 39 = 0or (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
10. Question
(X1/4 )2/625 =169/X3/2
Y4/3* Y2/3*2786 =7*Y3Ans:2
X1/2 /625 =169/X3/2X2 = 625*169X= ± (25*13) = ±325
Y6/3*2786 =7*y3
Y =2786/7 =398
X<Y
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