# Set-27 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 questions, two equations I and II are given. You have to solve both the equations and give Answer as,

1.
I.√(1225)x + √(1089) =0
II.(625)1/4 y + (343)1/3 = 0

2.
I. 25x2 – 45x + 14 =0
II.48y2 -176y – 64 =0

3.
I. 72x2 -177x +108 =0
II. 5y2 + 24y + 27 =0

4.
I. x2 -11x +30 =0
II. y2 -13y + 42 =0

5.
I. 25x2 +32x -36 =0
II. 57y2 -25y-42 =0

6.
I.2x^2 + 19x + 45 = 0
II.2y^2 + 11y + 12 = 0

7.
I.3x^2 – 13x + 12 = 0
II.2y^2 – 15y + 28 = 0

8.
I.x^2 = 16
II.2y^2 – 17y + 36 = 0

9.
I.6x^2 + 19x + 15 = 0
II.3y^2 + 11y + 10 = 0

10.
I.2x^2 – 11x + 15 = 0
II.2y^2 – 11y + 14 = 0

Directions:1-10) In the following questions, two equations I and II are given. You have to solve both the equations and give Answer as,

##### 1. Question

I.√(1225)x + √(1089) =0
II.(625)1/4 y + (343)1/3 = 0

Ans:
I.√(1225)x + √(1089) =0
35x + 33 = 0
35x = -33
X= -33/35 = -0.94

II.(625)1/4 y + (343)1/3 = 0
5y+7 =0
Y= -7/5 = -1.4
x>y

##### 2. Question

I. 25x2 – 45x + 14 =0
II.48y2 -176y – 64 =0

Ans:
I.25x2 – 45x + 14 =0
25x2 – 10x – 35x + 14 =0
5x(5x-2) -7(5x-2) =0
(5x-7) (5x-2) = 0
X= 7/5 , 2/5 =1.4, 0.4

II.48y2 -176y – 64 =0
48y2 -192y +16y – 64 =0
48y(y-4)+16 (y-4)=0
(48y + 16) (y-4) =0
Y= – 16/48, 4 = -0.33, 4
Can’t be determined

##### 3. Question

I. 72x2 -177x +108 =0
II. 5y2 + 24y + 27 =0

Ans:
I.72x2 -177x +108 =0
72x2 -81x -96x +108 =0
9x(8x-9)-12(8x-9) =0
(9x-12)(8x-9)=0
X=12/9 , 9/8 =1.33, 1.125

II.5y2 + 24y + 27 =0
5y2 + 15y + 9y + 27 =0
5y(y+3)+9(y+3) =0
(5y+9) (y+3) =0
Y= -9/5 , -3 = -1.8, -3
X > y

##### 4. Question

I. x2 -11x +30 =0
II. y2 -13y + 42 =0

Ans:
I.x2 -11x +30 =0
x2 -5x -6x +30 =0
x(x-5)-6 (x-5) =0
(x-6) (x-5) =0
X=6, 5

II.y2 -13y + 42 =0
y2 – 6y – 7y + 42 =0
y(y-6)-7(y-6) =0
(y-7)(y-6) =0
Y= 7, 6
x ≤ y

##### 5. Question

I. 25x2 +32x -36 =0
II. 57y2 -25y-42 =0

Ans:
I.25x2 +32x -36 =0
25x2 -18x + 50x -36 =0
X(25x-18)+2 (25x-18)=0
(x+2) (25x-18) = 0
X =-2, 18/25 = -2, 0.72

II.57y2 -25y-42 =0
57y2 +38y-63y -42 =0
19y (3y+2)- 21(3y+2) =0
(19y-21) (3y+2) =0
y= 21/19, -2/3 = 1.105, -0.66
Can’t be determined

##### 6. Question

I.2x^2 + 19x + 45 = 0
II.2y^2 + 11y + 12 = 0

Ans:
I.2x^2 + 19x + 45 = 0
2 × 45 = 90 = (10 × 9)
(10 + 9 = 19) x = (-10/2), (-9/2) (dividing by co efficient of x^2 and changing signs)
x = -5, -4.5

II.2y^2 + 11y + 12 = 0
2 × 12 = 24 (8 × 3 = 24) (8 + 3 = 11)
y = (-8/2), (-3/2) ) (dividing by co efficient of y^2 and changing signs)
y = -4, -1.5
Hence x < y

##### 7. Question

I.3x^2 – 13x + 12 = 0
II.2y^2 – 15y + 28 = 0

Ans:
I.3x^2 – 13x + 12 = 0
12 × 3 = 36 (-9 × -4 = 36) (-9 – 4 = -13)
x = 9/3, 4/3 (dividing by co efficient of x^2 and changing signs)
x = 3, 4/3

II.2y^2 – 15y + 28 = 0
2 × 28 = 56 (-8 × -7 = 56)
(-8 -7 = -15) (Dividing by co efficient of y^2 and changing signs)
y = 4, 3.5
Hence x< y

##### 8. Question

I.x^2 = 16
II.2y^2 – 17y + 36 = 0

Ans:
I.x^2 = 16
x = ±4

II.2y^2 – 17y + 36 = 0
2 × 36 = 72 (-9 × -8 = 72)
(-9 -8 = -17) y = 9/2, 8/2(dividing by co efficient of y^2 and changing signs)
y = 4.5, 4
Hence x ≤ y

##### 9. Question

I.6x^2 + 19x + 15 = 0
II.3y^2 + 11y + 10 = 0

Ans:
I.6x^2 + 19x + 15 = 0
6 × 15 = 90 (10 × 9 = 90) (10 + 9 = 19)
x = -10/6, -9/6 (dividing by co efficient of x^2 and changing signs)
x = -5/3, -3/2 = -1.66, -1.5

II.3y^2 + 11y + 10 = 0
3 × 10 = 30 (6 × 5 = 30) (6 + 5 = 11)
y = -6/3, -5/2 (dividing by co efficient of y^2 and changing signs)
y = -1.6, -2
Hence x ≥ y

##### 10. Question

I.2x^2 – 11x + 15 = 0
II.2y^2 – 11y + 14 = 0

Ans:
I.2x^2 – 11x + 15 = 0
2 × 15 = 30 (-6 × -5 = 30) (-6 – 5 = -11)
x = -6/2, -5/2 (dividing by co efficient of x^2 and changing signs)
x = 3, 2.5

II.2y^2 – 11y + 14 = 0
2 × 14 = 28 (-7 × -4 = 28) (-7 -4 = -11)
y = 7/2, 4/2 (dividing by co efficient of y^2 and changing signs)
y = 3.5, 2
Hence relationship cannot be established 