# Set-23 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: 1-5) In the following questions, two equations numbered are given in variables x and y. Solve both the equations and find out the relationship between x and y. Then give answer accordingly-

1.
I. 12p2 – 5p – 3 = 0,
II. 3q2 – 11q + 6 = 0

2.
I. 6p2 + 7p + 2 = 0,
II. 15q2 – 38q – 40 = 0

3.
I. 3p2 – 25p + 52 = 0
II. 2q2 – 7q + 3 = 0

4.
I. p2 = 1156
II. q = √1156

5.
I. p2 – √3969 = √6561,
II. q2 – √1296 = √4096

Directions:6-10) In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give an answer

6.
I.  (x+3) (y+2)=12
II. 2xy+4x+5y=11

7.
I. (3x-2)/y = (3x+6)/(y+16)
II. (x+2)/(y+4) = (x+5)/(Y+10)

8.
I.  x2+20x+4=50-25x
II. y2-10y-24=0

9.
I. (x2-10x+16)/(x2 -12x +24) = 2/3
II. y2-y-20=0

10.
a)785+x=846-72
b)y^2=(1862-1726+23)

• Directions: 1-5) In the following questions, two equations numbered are given in variables x and y. Solve both the equations and find out the relationship between x and y. Then give answer accordingly-

##### 1. Question

I. 12p2 – 5p – 3 = 0,
II. 3q2 – 11q + 6 = 0

Ans:5
12p2 – 5p – 3 = 0
12p2 + 4p – 9p – 3 = 0
Gives p = -1/3, 3/4
3q2 – 11q + 6 = 0
3q2 – 9q – 2q + 6 = 0
Gives q = 2/3, 3
Put all values on number line and analyze the relationship
-1/3… 2/3… 3/4… 3

• ##### 2. Question

I. 6p2 + 7p + 2 = 0,
II. 15q2 – 38q – 40 = 0

Ans:5
6p2 + 7p + 2 = 0
6p2 + 4p + 3p + 2 = 0
Gives p = -2/3, -1/2
15q2 – 38q – 40 = 0
15q2 + 12q – 50q – 40 = 0
Gives q = -4/5, 10/3
Put all values on number line and analyze the relationship
-4/5… -2/3… -1/2… 10/3

• ##### 3. Question

I. 3p2 – 25p + 52 = 0
II. 2q2 – 7q + 3 = 0

Ans:1
3p2 – 25p + 52 = 0
3p2 – 12p – 13p + 52 = 0
Gives p = 4, 13/3
2q2 – 7q + 3 = 0
2q2 – 6q – q + 3 = 0
So q = 1/2, 3
Put all values on number line and analyze the relationship
1/2… 3… 4… 13/3

p > q

• ##### 4. Question

I. p2 = 1156
II. q = √1156

Ans:4
p2 = 1156
So p = -34, 34
q = √1156
So q = 34
Put all values on number line and analyze the relationship
-34… 34

p ≤ q

• ##### 5. Question

I. p2 – √3969 = √6561,
II. q2 – √1296 = √4096

Ans:5
p2 – √3969 = √6561
p2 – 63 = 81
p2 = 144
So p = -12, 12
q2 – √1296 = √4096
q2 – 36 = 64
q2 = 100
So q = -10, 10
Put all values on number line and analyze the relationship
-12… -10….10…. 12

• ##### 6. Question

Directions:6-10) In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give an answer

I.  (x+3) (y+2)=12

II. 2xy+4x+5y=11

Ans:5
xy+3y+2x +6 =12

2xy+6y+4x=12—-(i)

2xy+5y+4x=11 —- (ii)

From eq. (i) — (ii)

Y = 1

From eq. (i)

x=1

x = y

• ##### 7. Question

I. (3x-2)/y = (3x+6)/(y+16)

II. (x+2)/(y+4) = (x+5)/(Y+10)

Ans:2
(3x-2)/y = (3x+6)/(y+16)

48x-8y = 32 —- (i)

(x+2)/(y+4) = (x+5)/(y+10)

y = 2x —- (i)

From Equation (i) & (ii)

x=1, y=2

x<y

• ##### 8. Question

I.  x2+20x+4=50-25x

II. y2-10y-24=0

Ans:5
x2+20x+4=50-25x

x2+45x-46=0

x2-x+46x-46=0

x(x-1)+ 46 (x-1) =0

(x-1)(x+46)=0

X= -46 and 1

y2-10y-24=0

y2+2y -12y -24=0

y(y+2) – 12 (y+2) =0

(y-12) (y+2) =0

Y = 12 and -2

Relationship cannot be established

• ##### 9. Question

I. (x2-10x+16)/(x2 -12x +24) = 2/3

II. y2-y-20=0

Ans:5
(x2-10x+16)/(x2 -12x +24) = 2/3

3x2-30x+48=2x2-24x+48

X2-6x=0

(x) (x-6) =0

X= 6, 0

y2-y-20=0

y2-5y+4y-20=0

y(y-5)+4(y-5)=0

(y+4)(y-5) =0

Y = -4, 5

Relationship cannot be established

• ##### 10. Question

a)785+x=846-72

b)y^2=(1862-1726+23)

Ans:4
a)785+x=846-72

785+x=846-49

x=797-785

x=12

b)y^2=(1862-1726+23)

y^2=144

y=12 and -12

Hence x≥y