# Set-18 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 the following question, two equations I and II are given. Solve both the equations carefully & answer the questions given below:

1.

I. 8x2 – 49x + 45 = 0

II. 8y2 – y – 9 = 0

2.

I. 42x – 17y = -67

II. 7x + 12y = -26

3.

I .x2 – 8x + 15 = 0

II. 2y2 – 21y + 55 = 0

4.

I. x2 + 12x + 32 = 0

II. 2y2 + 15y + 27 = 0

5.

I. 6x2 – 17x + 12 = 0

II. 7y2 – 13y + 6 = 0

6.

I.11x + 5y = 117

II.7x + 13y = 153

7.

I.6x2 + 51x + 105 = 0

II.2y2 + 25y + 78 = 0

8.

I.6x + 7y = 52

II.14x + 4y = 35

9.

I.x2 + 11x + 30 = 0

II.y2 + 12y + 36 = 0

10.

I.2x2 + x – 1 = 0

II.2y2 – 3y + l = 0

Directions:1-10) In the following question, two equations I and II are given. Solve both the equations carefully & answer the questions given below:

##### 1. Question

I. 8x2 – 49x + 45 = 0

II. 8y2 – y – 9 = 0

Ans: 3
8x2 – 49x + 45 = 0

8x2-40x-9x+45=0

8x(x-5) – 9 (x-5) =0

(8x-9) (x-5) =0

X =9/8, 5

8y2 – y – 9 = 0

8y2+8y-9y-9=0

8y(y+1) -9 (y+1) =0

(8y-9) (y-+1) = 0

Y= 9/8,-1

X≥ Y

##### 2. Question

I. 42x – 17y = -67

II. 7x + 12y = -26

Ans:2
42x – 17y = -67 ——- 1

7x + 12y = -26 ——– 2

X = -2 Y= -1

X<Y

##### 3. Question

I .x2 – 8x + 15 = 0

II. 2y2 – 21y + 55 = 0

Ans:4
x2 – 8x + 15 = 0

x2-5x-3x+15=0

x(x-5) -3 (x-5) =0

(x-3) (x-5) =0

X =5, 3

2y2 – 21y + 55 = 0

2y2-10y-11y+55 = 0

2y (y-5) -11 (y-5) =0

(2y-11) (y-5) =0

Y =5, 11/2

x ≤ y

##### 4. Question

I. x2 + 12x + 32 = 0

II. 2y2 + 15y + 27 = 0

Ans:5
x2 + 12x + 32 = 0

x2+8x+4x+32=0

x(x+8) + 4 (x+8) =0

(x+4) (x+8) =0

X =-4,-8

2y2 + 15y + 27 = 0

2y2+6y+9y+27 =0

2y (y+3) +9 (y+3) =0

(2y+9) (y+3) =0

Y = -9/2 ,-6/2 =-4.5,-3

x = y or relation cannot be established

##### 5. Question

I. 6x2 – 17x + 12 = 0

II. 7y2 – 13y + 6 = 0

Ans:1
6x2 – 17x + 12 = 0

6x2-9x-8x+12=0

3x (2x-3) – 4 (2x-3) =0

(3x-4) (2x-3) =0

X =3/2, 4/3

7y2 – 13y + 6 = 0

7y2-7y -6y+6 =0

7y (y-1) -6 (y-1) =0

(7y-6) (y-1) =0

Y =6/7, 1

X>Y

##### 6. Question

I.11x + 5y = 117

II.7x + 13y = 153

Ans:2
eqn (I) × 7

77x + 35y = 819 —(III)

eqn (II) × 11

77x + 143y = 1683——(IV)

On solving (III) & (IV) we get,

– 108y = – 864

y = 8, x = 7 i.e., x < y

##### 7. Question

I.6x2 + 51x + 105 = 0

II.2y2 + 25y + 78 = 0

Ans:1
6x2 + 21x + 30x + 105 = 0

x = -5, – 7/2

2y2 + 12y + 13y + 78 = 0

y =-13/2, – 6

x > y

##### 8. Question

I.6x + 7y = 52

II.14x + 4y = 35

Ans:2
Eqn (I) × 4

Eqn (II) × 7

24x + 28y = 208 —- (III)

98x + 28y = 245 —— (IV)

On solving (III) & (IV) we get,

– 74x = – 37

x =1/2, y = 7

x < y

##### 9. Question

I.x2 + 11x + 30 = 0

II.y2 + 12y + 36 = 0

Ans:3
x2 + 5x + 6x + 30 = 0

X(x + 5) + 6(x + 5) = 0

(x + 5) (x + 6) = 0

x = – 5, – 6

y2 + 12y + 36 = 0

y(y + 6) + 6(y + 6) = 0

( y + 6) (y+6) = 0

y = – 6, -6

x ≥ y

##### 10. Question

I.2x2 + x – 1 = 0

II.2y2 – 3y + l = 0

Ans:4
2x2 + 2x – x – 1 = 0

2x(x + 1) – 1(x + 1) = 0

(2x – 1) (x + 1) = 0

X=  1/2 ,-1

2y2 – 2y – y + 1 = 0

2y(y – 1) – 1(y – 1) = 0

(2y – 1)(y – 1) = 0

Y= 1/2,1

ie x ≤ y