Set-16 Quadratic Equations (Inequalities) For SBI PO and SBI Clerk 2019 | Must Go Through These Questions

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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 the following questions, two equations I and II are given. You have to solve both the equations.

1.

1. p2 – 18p + 72= 0
2. 5q2 – 18q + 9 = 0

2.

• p2 = 4
• 3q2 – 4q – 4 = 0

3.

• 6p2 – 5p – 6 = 0
• 2q2 – 13q + 20 = 0

4.

1. 2p2 – 5p = 0
2. 3q2 – 7q – 6 = 0

5.

• 2p2 + 5p + 2= 0
• 2q2 + 19q + 45 = 0

Directions:6-10) In each of the following questions, two equations (i) and (ii) are given. You have to solve them and find the correct option.

6.

i) 3x2-23x+44=0
ii) y2-23y+132=0

7.

i) x2-6√3x-480=0
ii) y2-11√2y-420=0

8.

i) 7x-5y-74=0
ii) 3x+2y-301=0

9.

i) x(4/3)/289=25/x(2/3)
ii) y(4/5)/4913=125/y(11/5)

10.

i) 2x2+8x-42=0
ii) 6y2-101y+33=0

1. Directions: 1-5)In the following questions, two equations I and II are given. You have to solve both the equations.

1. Question
1. p2 – 18p + 72= 0
2. 5q2 – 18q + 9 = 0
Ans:
p2 – 18p + 72= 0
(p-12)(p-6) = 0
Gives p = 6, 12
5q2 – 18q + 9 = 0
5q2 – 15q – 3q + 9 = 0

5q (q-3) – 3(q-3) =0

(5q-3) (q-3) =0
Gives q = 3/5, 3
Put on number line
3/5   3    6  12

P > q

2. 2. Question

• p2 = 4
• 3q2 – 4q – 4 = 0

Ans:
p2 = 4
Gives p = 2 , -2
3q2 – 4q – 4 = 0
3q2 – 6q + 2q – 4 = 0
Gives q = -2/3, 2
Put on number line
-2      -2/3        2
So no relation

3. 3. Question

• 6p2 – 5p – 6 = 0
• 2q2 – 13q + 20 = 0

Ans:
6p2 – 5p – 6 = 0
6p2 – 9p + 4p – 6 = 0
Gives p = -2/3, 3/2
2q2 – 13q + 20 = 0
2q2 – 8q – 5q +20 = 0
Gives q = 4, 5/2
Put on number line
-2/3   3/2    5/2    4

P < q

4. 4. Question
1. 2p2 – 5p = 0
2. 3q2 – 7q – 6 = 0
Ans:
2p2 – 5p = 0
p(2p-5) = 0
Gives p = 0, 5/2
3q2 – 7q – 6 = 0
3q2 – 9q + 2q – 6 = 0
Gives q = -2/3, 3
Put on number line
-2/3    0   5/2         3

There is no relation

5. 5. Question

• 2p2 + 5p + 2= 0
• 2q2 + 19q + 45 = 0

Ans:
2p2 + 5p + 2= 0
2p2 + 4p + p + 2= 0
Gives p = -1/2, -2
2q2 + 19q + 45 = 0
2q2 + 10q + 9q + 45 = 0
Gives q= -10/2, -9/2
Put on number line
-10/2     -9/2    -2     -1/2

P > q

Directions:6-10) In each of the following questions, two equations (i) and (ii) are given. You have to solve them and find the correct option.

6. Question

i) 3x2-23x+44=0

ii) y2-23y+132=0

Ans:
i) 3x2-23x+44=0

3x2-12x-11x+44=0

(x-4)(3x-11)=0

x= 4 or 11/3

ii) y2-23y+132=0

(y-12)(y-11)=0

y= 12 or 11

Thus x<y

6. 7. Question

i) x2-6√3x-480=0

ii) y2-11√2y-420=0

Ans:
i) x2-6√3x-480=0

x2-6x-160=0

(x-16)(x+10)=0

x= 16 or -10

ii) y2-11√2y-420=0

y2– 11y- 210=0

(y-21)(y+10)=0

y=21 or -10

Hence The relationship cannot be determined.

7. 8. Question

i) 7x-5y-74=0

ii) 3x+2y-301=0

Ans:
7x-5y-74=0 ………… (1)

3x+2y-301=0 …………….. (2)

After solving (1) and (2), we have

x= 57 and y= 65

x < y

8. 9. Question

i) x(4/3)/289=25/x(2/3)

ii) y(4/5)/4913=125/y(11/5)

Ans:
i) x(4/3)/289=25/x(2/3)

x(4/3)*x(2/3)=7225

x2= 7225

x=85 and -85

ii) y(4/5)/4913=125/y(11/5)

y(15/5)=125*4913

y= 85

Thus x ≤ y

9. 10. Question

i) 2x2+8x-42=0

ii) 6y2-101y+33=0

Ans:
i) 2x2+8x-42=0

x2+4x-21=0

(x-3)(x+7)=0

x=3 or -7

ii) 6y2-101y+33=0

6y2-2y-99y+33=0

(3y-1)(2y-33)=0

y=1/3 or 33/2

Hence the relationship cannot be determined.