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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) **Two equations (I) and (II) are given in each questions. On the basis of these questions, you have to decide the relation between p and q and give answer**

1.

I.10p^{2} + 39p – 88 = 0

II.21q^{2} + 41q – 40 = 0

2.

I.14p^{2} – 43p + 20 = 0

II.33q^{2} + 72q + 12 = 0

3.

I.56p^{2} + 97p + 42 = 0

II.99q^{2} – 64q + 5 = 0

4.

I.16p^{2} – 40p + 25 = 0

II.25q^{2} – 40q + 16 = 0

5.

I.15p^{2} + 38p + 24 = 0

II.20q^{2} + 49q + 30 = 0

Directions:6-10) **In the following questions two equations I and II are given. You have to solve both the equations and give answer:**

6.

I) 6x²-12 x+6=0

II) 3y²-8y+5=0

7.

I) 5x²+50x+105=0

II) 9y²+30y+25=0

8.

I) 2x²-x-28=0

II) 3y²-14y-24=0

9.

I) 4x²+21x+27=0

II) 5y²-22y-15=0

10.

I) 2x²-13y+21=0

II) y²-32y+231=0

**Check your Answers below:**

Directions:1-5)

**Two equations (I) and (II) are given in each questions. On the basis of these questions, you have to decide the relation between p and q and give answer**##### 1. Question

I.10p

^{2}+ 39p – 88 = 0II.21q

^{2}+ 41q – 40 = 0Ans:5

I.10p^{2}+ 39p – 88 = 0or, 10 p

^{2}– 16p + 55p – 88 = 0or, 2p(5p – 8) + 11(5p – 8) = 0

or, (2p + 11) (5p – 8) = 0

p = -11/2 or 8/5

II.21 q

^{2 }+ 41q – 40 = 0or, 21 q

^{2}+ 56q – 15q – 40 = 0or, 7q(3q + 8) – 5(3q + 8) = 0

or, (7q – 5) (3q + 8) = 0

q = 5/7 or -8/3

**We can’t get specific relationship between p and q.**##### 2. Question

I.14p

^{2}– 43p + 20 = 0II.33q

^{2}+ 72q + 12 = 0Ans:1

I.14 p^{2 }– 43p + 20 = 0or, 14 p

^{2}– 35p – 8p + 20 = 0or, 7p(2p – 5) – 4(2p – 5) = 0

or, (7p – 4) (2p – 5) = 0

p = 4/7 or 5/2

II.33 q

^{2}+ 72q + 12 = 0or, 33 q

^{2}+ 6q + 66q + 12 = 0or, 3q(11q + 2) + 6(11q + 2) = 0

or, (3q + 6) (11q + 2) = 0

q = -2 or -2/11

**Hence p > q**.##### 3. Question

I.56p

^{2}+ 97p + 42 = 0II.99q

^{2}– 64q + 5 = 0Ans:2

I.56 p^{2}+ 97p + 42 = 056 p

^{2}+ 49p + 48p + 42 = 0or, 7p(8p + 7) + 6(8p + 7) = 0

or, (7p + 6) (8p + 7) = 0

p = -6/7 or -7/8

II.99 q

^{2}– 64q + 5 = 0or, 99 q

^{2}– 9q – 55q + 5 = 0or, 9q (11q – 1) – 5(11q – 1) = 0

or, (9q – 5) (11q – 1) = 0

q = 5/9 or 1/11

**Hence p < q.**##### 4. Question

I.16p

^{2}– 40p + 25 = 0II.25q

^{2}– 40q + 16 = 0Ans:1

I.16 p^{2}– 40p + 25 = 0or, 16 p

^{2}– 20p – 20p + 25 = 0or, 4p(4p – 5) – 5(4p – 5) = 0

or, (4p – 5) (4p – 5) = 0

p = 5/4, 5/4

II.25 q

^{2}– 40q + 16 = 0or, 25 q

^{2 }– 20q – 20q + 16 = 0or, 5q(5q – 4) – 4(5q – 4) = 0

or, (5q – 4) (5q – 4) = 0

q = 4/5, 4/5

**Hence p > q**.##### 5. Question

I.15p

^{2}+ 38p + 24 = 0II.20q

^{2}+ 49q + 30 = 0Ans:5

I.15 p^{2}+ 38p + 24 = 0or, 15 p

^{2}+ 20p + 18p + 24 = 0or, 5p(3p + 4) + 6(3p + 4) = 0

or, (5p + 6) (3p + 4) = 0

p = -6/5 or -4/3

II.20 q

^{2}+ 49q + 30 = 0or, 20 q

^{2}+ 24q + 25q + 30 = 0or, 4q(5q + 6) + 5(5q + 6) = 0

or, (4q + 5) (5q + 6) = 0

q = -5/4 or -6/5

**We can’t get specific relationship between p and q.**Directions:6-10)

**In the following questions two equations I and II are given. You have to solve both the equations and give answer:**##### 6. Question

I) 6x²-12 x+6=0

II) 3y²-8y+5=0

Ans:3

6x²-6x-6x+6=0X=6/6,6/6 =1, 1

3y²-3y-5y+5=0

Y=5/3, 3/3 = 1.66, 1

x ≤ y

##### 7. Question

I) 5x²+50x+105=0

II) 9y²+30y+25=0

Ans:2

5x²+50x+105=05x²+15x+35x+105=0

X=-15/5,-35/5 = -3, -7

9y²+30y+25=0

9y²+15y+15y+25=0

Y=-15/9,-15/9 = -5/3, -5/3 = -1.66, -1.66

x < y

##### 8. Question

I) 2x²-x-28=0

II) 3y²-14y-24=0

Ans:5

2x²-8x+7x-28=0X= 8/2, -7/2 = 4, -3.5

3y²-18y+4y-24=0

Y= 18/3, -4/3 = 6.66, -1.33

Cannot be determined

##### 9. Question

I) 4x²+21x+27=0

II) 5y²-22y-15=0

Ans:2

4x²+12x+9x+27=0X=-12/4,-9/4 = -3, -2.25

5y²-25y+3y-15=0

Y=25/2, -3/5 = 12.5, -0.6

x < y

##### 10. Question

I) 2x²-13y+21=0

II) y²-32y+231=0

Ans:2

2x²-6x-7x+21=0X= 6/2 ,7/2= 3, 3.5

y²-11y-21y+231=0

y=11, 21

x < y