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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:1-10) In the following questions, two equations I and II are given. You have to solve both the equations and give Answer as,
1.
- 4p² + 8p + 3 = 0
- 4q² – 29q + 45 = 0
2.
- 2p² – 23p + 21 = 0
- q² + 42q + 272 = 0
3.
- 5p² – 26p + 21 = 0
- 2q² – 17q + 21 = 0
4.
- p² – 21p + 104 = 0
- q² – 33q + 260 = 0
5.
- p² – 31p + 240 = 0
- q² – 28q + 195 = 0
6.
I.3p2 + 13p + 14 = 0
II.3q2 + 11q + 10 = 0
7.
I.49p2 – 84p + 36 = 0
II.25q2 – 30q + 9 = 0
8.
I.3p + 4q = 49
II.5p + 8q = 91
9.
I.p + (1 / p) = 17 / 4
II.4q2 + 4 + 17q = 0
10.
I.p2 – 9p + 18 = 0
II.2q2 – 5q = 3
Check your Answers below:
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
- 4p² + 8p + 3 = 0
- 4q² – 29q + 45 = 0
Ans:2
4p² + 8p + 3 = 04p2+2p+6p+3 =0
2p (2p+1)+ 3(2p+1) =0
(2p+3) (2p+1)= 0
p = -0.5, -1.5
4q² – 29q + 45 = 04q2-20q-9q+45 =0
4q(q-5) -9 (q-5) =0
(4q-9) (q-5) =0
q = 2.25, 5P < q
2. Question
- 2p² – 23p + 21 = 0
- q² + 42q + 272 = 0
Ans:1
2p² – 23p + 21 = 02p2-21p-2p +21 =0
2p (p-1) -21 (p-1) =0
(2p-21)(p-1) =0
p = 10.5, 1
q² + 42q + 272 = 0q2+8q+34q+272 =0
q(q+8)+34 (q+8) =0
(q+8)(q+34)=0
q = -8, -34P > q
3. Question
- 5p² – 26p + 21 = 0
- 2q² – 17q + 21 = 0
Ans:5
5p² – 26p + 21 = 05p2-5p-21p+21=0
(5p-21) (p-1) =0
p = 4.2, 0.2
2q² – 17q + 21 = 02q2-14q-3q+21 =0
2q (q-7) -3(q-21) =0
(2q-3) (q-7) =0
q = 7, 1.5
Relationship cannot be determined
4. Question
- p² – 21p + 104 = 0
- q² – 33q + 260 = 0
Ans:4
p² – 21p + 104 = 0P2-13p-8p+104 =0
(p-8) (p-13) =0
p = 13, 8
q² – 33q + 260 = 0q2– 13q- 20q + 260 =0
(q-13) (q-20) =0
q = 13, 20P ≤ q
- p² – 31p + 240 = 0
- q² – 28q + 195 = 0
5. Question
Ans:3
p² – 31p + 240 = 0p2– 15p- 16p + 240 =0
(p-15) (p-16) =0
p = 15, 16
q² – 28q + 195 = 0q2 – 13q – 15q +195 =0
(q-13) (q-15) =0
q = 13, 15P ≥ q
6. Question
I.3p2 + 13p + 14 = 0
II.3q2 + 11q + 10 = 0
Ans:5
I.3p2 + 13p + 14 = 0Or, (3p + 7)(p + 2) = 0
p = -2 or –(7 / 3)
II.3q2 + 11q + 10 = 0
Or, (q + 2)(3q + 5) = 0
∴ q = -2 or – (5 / 3)
Hence p ≤ q
7. Question
I.49p2 – 84p + 36 = 0
II.25q2 – 30q + 9 = 0
Ans:2
I.49p2 – 84p + 36 = 0Or, 49p2 – 42p – 42p + 36 = 0
Or, (7p – 6)(7p – 6) = 0
p = 6 / 7
II.25q2 – 30q + 9 = 0
Or, (5q – 3)2 = 0
∴ q = 3 / 5
Hence p > q
8. Question
I.3p + 4q = 49
II.5p + 8q = 91
Ans:3
Here, p = q = 79. Question
I.p + (1 / p) = 17 / 4
II.4q2 + 4 + 17q = 0
Ans:2
I.p + (1 / p) = 17 / 4 = 4(1 / 4)p = 4 or 1 / 4
II.4q2 + 4 + 17q = 0
Or, 4q2 + 16q + q + 4 = 0
Or, (q + 4)(4q + 1) = 0
q = -4, or – (1 / 4)
Hence p > q
10. Question
I.p2 – 9p + 18 = 0
II.2q2 – 5q = 3
Ans:4
I.p2 – 9p + 18 = 0Or, (p – 6)(p – 3) = 0
p = 6 or 3
II.2q2 – 5q – 3 = 0
Or, (q – 3)(2q + 1) = 0
∴ q = – (1 / 2) or 3
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