Set-28 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.

Directions:1-10) In each of the following questions, two equations(i) and (ii) are given. You have to solve them and find the correct option.

1.
a) 2x2-23x-70=0
b) 2y2-7y-72=0

2.
a) 45x2-43x+10=0
b) 17y2+48y-9=0

3.
a) 14x+16y=10
b) 12x-10y=56

4.
a) 3x2-16x +20=0
b) 3y2-17y+24=0

5.
a) 3x^2-24x +36=0
b) 2.5y2 +5y -20=0

6.
a) 5-52x+96=0
b) 5-22y +24=0

7.
a) 6x-52√x+112=0
b) 4y-30√y+56=0

8.
a) 3x+23y=184
b) 4x+11y=125

9.
a) 3x =19683
b)2x =1024

10.
a) x2 -5.8x + 8.41=0
b) y2 – 3.8y + 3.12=0

Directions:1-10) In each of the following questions, two equations(i) and (ii) are given. You have to solve them and find the correct option.

a) 2x2-23x-70=0
b) 2y2-7y-72=0

Ans: 5
a)2x2-28x+5x-70=0
2x(x-14) +5(x-14) =0
x=14 and x=-5/2
x=14 and x=-2.5

b) 2y2-7y-72=0
2y2+9y-16y-72=0
2y(y-8) +9(y-8) =0
y=8 and y=-9/2
y=8 and y=-4.5
Hence x=y or cannot be determined

2. Question

a) 45x2-43x+10=0
b) 17y2+48y-9=0

Ans: 1
a) 45x2-43x+10=0
45x2-25x-18x+10=0
(9x-5)(5x-2)=0
x=5/9 and 2/5
x=0.5 and 0.4

b) 17y2+48y-9=0
17y2+51y-3y-9=0
(y+3)(17y-3)=0
y=-3 and 3/17
y=-3 and 0.17
Hence x>y

3. Question

a) 14x+16y=10
b) 12x-10y=56

Ans: 1
14x+16y=10……… (1)
Multiply (1) with 6, then we have
84x+96y=60 ………… (2)
12x-10y=56 …………. (3)
Multiply (3) with 7, then
84x-70y=392 ………. (4)
x= 3 and y= – 2
Hence x > y

4. Question

a) 3x2-16x +20=0
b) 3y2-17y+24=0

Ans: 5
a)3x^2-16x +20=0
3x^2-10x-6x +20=0
3x(x-2)-10(x-2) =0
x=10/3 and 2

b) 3y^2-17y+24=0
3y^2-9y -8y+24=0
3y(y-3)-8(y-3) =0
y=8/3 and 3
Hence x=y Or cannot be determined

5. Question

a) 3x^2-24x +36=0
b) 2.5y2 +5y -20=0

Ans: 4
a) 3x^2-24x +36=0
x^2-8x +12=0
x^2-2x-6x +12=0
x(x-2)-6(x-2)=0
x=2 and 6

b) 2.5y^2+5y -20=0
y^2+2y -8=0
(y-2)(y+4)=0
y=2 and -4
Hence x ≥y

6. Question

a) 5-52x+96=0
b) 5-22y +24=0

Ans: 4
a)5x2-52x+96=0
5x2 -12x-40x+96=0
5x(x-8)-12(x-8) = 0
x=8 and 12/5

b) 5y2 -22y +24=0
5y2 -10y-12y +24=0
5y(y-2)-12(y-2) = 0
y=2 and 12/5
Hence x ≥ y

7. Question

a) 6x-52√x+112=0
b) 4y-30√y+56=0

Ans: 4
a) 6x- 52√x + 112=0
6x-24√x-28√x+112=0
6√x(√x-4)-28(√x-4) = 0
√x=14/3 and 4
x=196/9 and 16

b) 4y-30√y + 56=0
4y-16√y-14√y+56=0
(4√y-14)(√y-4) = 0
√y= 7/2 and 4
y=49/4 and 16
Hence x ≥y

8. Question

a) 3x+23y=184
b) 4x+11y=125

Ans: 1
a) 3x+23y=184……………….(1)
b) 4x+11y=125.……………….(2)

Multiply equation (1) by 4
12x+92y=736
Multiply the equation (2) by 3
12x+33y=375
After solving these two equations, we get
y= 6.12 and x=14.41
Hence x > y

a) 3x =19683
b)2x =1024

Ans: 2
a) 3x =19683
3x = 39
x=9

b)2y =1024
2y =210
y=10
Thus x<y

10. Question

a) x2 -5.8x + 8.41=0
b) y2 – 3.8y + 3.12=0

Ans: 1
a) x2 – 5.8x +8.41=0
x2 – 2.9x – 2.9x + 8.41=0
(x-2.9) (x-2.9) = 0
x=2.9 and 2.9

b) y2 – 3.8y + 3.12=0
y2 -1.2y-2.6y + 3.12=0
(y-1.2) (y-2.6) = 0
y= 1.2 and 2.6
Thus x>y