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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 each of the following questions, two equations (i) and (ii) are given. You have to solve them and find the correct option**.

1.

i) 2x^{2}-23x+56=0

ii) 3y^{2}+13y+4=0

2.

i) x^{2}-22x+117=0

ii) 5y^{2}+41y+42=0

3.

i) 2x^{2}-7x+5=0

ii) 2y^{2}+y-28=0

4.

i) x^{4}-[(9)^{9/2}/√x]=0

ii) (4/√y)+ (5/√y)= √y

5.

i) x^{2}+5x+4=0

ii) 3y^{2}-13y+12=0

Directions:6-10) **In the following questions, two equations numbered are given in variables p and q. You have to solve both the equations and find out the relationship between p and q. Then give answer accordingly****.**

6.

I. 3p^{2} – 17p + 10 = 0

II. 3q^{2} + 4q – 4 = 0

7.

I. 3p^{2} – 14p + 8 = 0

II. 3q^{2} – 20q + 12 = 0

8.

I. 3p^{2} – 19p + 28 = 0

II. 4q^{2} – 5q – 6 = 0

9.

I. 6p^{2} + 23p + 21 = 0

II. 3q^{2} – 14q – 5 = 0

10.

I. 2p^{2} – 7p + 3 = 0

II. 2q^{2} + 11q + 12 = 0

**Check your Answers below:**

Directions:1-5)

**In each of the following questions, two equations (i) and (ii) are given. You have to solve them and find the correct option**.##### 1. Question

i) 2x

^{2}-23x+56=0ii) 3y

^{2}+13y+4=0Ans:1

i) 2x^{2}-23x+56=02x

^{2}-16x-7x+56=0(2x-7)(x-8)=0

x= 7/2 or 8

ii) 3y

^{2}+13y+4=03y

^{2}+12y+y+4=0(3y+1)(y+4)=0

y= -1/3 or -4

Hence x >y

##### 2. Question

i) x

^{2}-22x+117=0ii) 5y

^{2}+41y+42=0Ans:1

i) x^{2}-22x+117=0x

^{2}-13x-9x+117=0(x-13)(x-9)=0

x=13 or 9

ii) 5y

^{2}+41y+42=05y

^{2}+35y+6y+42=0(y+7)(5y+6)=0

y=-7 or -6/5

Hence x >y

##### 3. Question

i) 2x

^{2}-7x+5=0ii) 2y

^{2}+y-28=0Ans:5

i) 2x^{2}-7x+5=02x

^{2}-2x-5x+5=0(x-1)(2x-5)=0

x=1 or 5/2

ii) 2y

^{2}+y-28=02y

^{2}+8y-7y-28=0(2y-7)(y+4)=0

y= -4 or 7/2

Hence the relationship cannot be determined

##### 4. Question

i) x

^{4}-[(9)^{9/2}/√x]=0ii) (4/√y)+ (5/√y)= √y

Ans:5

i) x^{4}-[(9)^{9/2}/√x]=0x

^{9/2}-9^{9/2}=0x

^{9/2}=9^{9/2}x=9

ii) (4/√y)+ (5/√y)= √y

9/√y=√y

y=9

Hence, x= y

##### 5. Question

i) x

^{2}+5x+4=0ii) 3y

^{2}-13y+12=0Ans:1

i) x^{2}+5x+4=0x

^{2}+4x+x+4=0(x+1)(x+4)=0

x= -1 or -4

ii) 3y

^{2}-13y+12=03y

^{2}-9y-4y+12=0(y-3)(3y-4)=0

y=4/3 or 3

Hence x< y

Directions:6-10)

**In the following questions, two equations numbered are given in variables p and q. You have to solve both the equations and find out the relationship between p and q. Then give answer accordingly****.**##### 6. Question

I. 3p

^{2}– 17p + 10 = 0

II. 3q^{2}+ 4q – 4 = 0Ans:3

3p^{2}– 17p + 10 = 03p

^{2}– 15p – 2p + 10 = 0Gives p = 2/3, 5

3q

^{2}+ 4q – 4 = 03q

^{2}+ 6q – 2q – 4 = 0Gives q = -2, 2/3

-2…. 2/3…… 5

p ≥ q

##### 7. Question

I. 3p

^{2}– 14p + 8 = 0

II. 3q^{2}– 20q + 12 = 0Ans:5

3p^{2}– 14p +8 = 03p

^{2}– 12p – 2p + 8 = 0Gives p = 2/3, 4

3q

^{2}– 20q + 12 = 03q

^{2}– 18q – 2q + 12 = 0Gives q = 6, 2/3

2/3….. 4….. 6

Relation cannot be determined

##### 8. Question

I. 3p

^{2}– 19p + 28 = 0

II. 4q^{2}– 5q – 6 = 0Ans:1

3p^{2}– 19p + 28 = 03p

^{2}– 12p – 7p + 28 = 0Gives p = 7/3, 4

4q

^{2}– 5q – 6 = 04q

^{2}– 8q + 3q – 6 = 0Gives q = -3/4, 2

-3/4…… 2…… 7/3…. 4

p > q

##### 9. Question

I. 6p

^{2}+ 23p + 21 = 0

II. 3q^{2}– 14q – 5 = 0Ans:2

6p^{2}+ 23p + 21 = 06p

^{2}+ 9p + 14p + 21 = 0Gives p = -7/3, -3/2

3q

^{2}– 14q – 5 = 03q

^{2}– 15q + q – 5 = 0Gives q = -1/3, 5

-7/3…… -3/2….. -1/3…… 5

p < q

##### 10. Question

I. 2p

^{2}– 7p + 3 = 0

II. 2q^{2}+ 11q + 12 = 0Ans:1

2p^{2}– 7p + 3 = 02p

^{2}– 6p – p + 3 = 0Gives p = 3, 1/2

2q

^{2}+ 11q + 12 = 02q

^{2}+ 8q + 3q + 12 = 0Gives q = -3/2, -4

-4……. -3/2…… 1/2….. 3

p > q