Quadratic Equation Test

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Quadratic Equation Test - 7

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Weekly Quiz Competition

Question 1
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Which of the following equations has –84 as discriminant?

A
2x² + 2x + 11 = 0

B
x² + x + 12 = 0

C
x² – 11x + 2 = 0

D
x² + x + 29 = 0

Solution

Discriminant = b² - 4ac
2x² + 2x + 11 = 0
D = 4 - 4 x 2 x 11
= 4 - 88 = - 84
Question 2
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Which of the following equations has as one of its solutions?

A
=

B
=

C
=

D
= 1

Solution

Put x =

= Hence is a solution of
Question 3
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Which of the following equations has -2 as one of its solutions?

A
(2y + 2)² = 49

B
(3y + 7)² = 64

C
(y + 1)² = 2

D
None of these

Solution

(27 + 2)² = 49
y² - 2 does not satisfy this
(3y + 7)² = 64
y = - 2 does not satisfy this
(y + 1)² = 2
y= -2 does not satisfy this.
(4) option i : e None of these.
Question 4
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Which of the following equations is same as 4x² - 5x - 3 = 0?

A

B

C

D

Solution

4x² - 5x - 3 = 0
x² - - = 0
= 0

Option (4)
Question 5
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Which of the following equations has 8 as one of its solutions?

A
(x + 3)² = 36

B
(x - 3)² = 25

C
(x + 4)² = 25

D
(x - 2)² = 16

Solution

(x + 3)² = 36
x = 8 is not a solution
(x - 3)² = 25
x = 8 gives
5² = 25
25 = 25
Hence x = 8 is a solution to this equation.
Question 6
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Which of the following equations has 9 as discriminant?

A
x² + 5x + 4 = 0

B
x² + 5x - 4 = 0

C
x² + 4x + 5 = 0

D
x² - 4x - 5 = 0

Solution

x² + 5x + 4 = 0
d = b² - 4ac
25 - 4 (4) 1
= 25 - 16 - 9
Option (1)
Question 7
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Which of the following equations has real and equal roots?

A
3x² - 17x + 20 = 0

B
2x² - 3x + 5 = 0

C
9x² - 24x + 16 = 0

D
2x² - x - 15 = 0

Solution

3x² - 17x + 20 = 0 for roots D = 0
D = 289 - 240 = 49
No equal roots.
(2) 2x² - 3x + 5 = 0
D = 9 - 40 = - 31
(3) 9x² - 24x + 16 = 0
d = 576 - 64 x 9
= 576 - 576 = 0
Hence real and equal roots.
Question 8
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Which of the following equations has the solution y = 2?

A
(2y + 1)² = 25

B
(3y - 1)² = 25

C
(2y + 7)²= 121

D
All of the above

Solution

(1) (2y + 1)² = 25
y = 2 satifies this
(2) (3y - 1)²= 25
y = 2 satisfies this
(3) (2y + 7)² = 121
y = 2 satisfies this
(4) All of the above.
Question 9
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Which of the following equations has no real roots?

A
x² - 9x + 20 = 0

B
8x² + 14x - 15 = 0

C
4x² - 18x + 20 = 0

D
11x² - 13x + 5 = 0

Solution

For no real roots D < 0
(1) D = 81 - 80 = 1 > 0
(2) 196 - 4 (8) (-15) > 0
(3) D = 324 - 320 > 0
(4) D = 169 - 220 < 0
Hence (4)
Question 10
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What will be the discriminant of the given quadratic equation?
3x² + 5x + 2 = 0

A
25

B
1

C
– 1

D
– 25

Solution

3x² + 5x + 2 = 0
D = 25 - 24 = 1
Question 11
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If the roots of the quadratic equation ax² + bx + c = 0 are real and distinct, then _____.

A
b² - 2ab = 0

B
b² - 4ac < 0

C
b² - 4ac > 0

D
b² + 4ac < 0

Solution

ax² + bx + c = 0
b² - 4ac > 0
Question 12
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What will be the discriminant of the given quadratic equation?
5x² + x + 7 = 0

A
- 138

B
- 139

C
- 140

D
- 141

Solution

5x² + x + 7 = 0
D = 1 - 4 x 5 x 7
= - 139
Question 13
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Which of the following equations has (2 +) as one of its solutions?

A
(3x – 6)² = 90

B
(5x – 4)² = 40

C
(4x – 2)² = 80

D
(4x – 5)² = 60

Solution

(3x - 6)² = 90
3x - 6 =
3x - 6 = 3
x = 2 +
Hence (1)
Question 14
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What will be the discriminant of the given quadratic equation?
2x² + 7x + 5 = 0

A
-9

B
- 7

C
7

D
9

Solution

2x² + 7x + 5 = 0
D = 49 - 4 x 2 x 5
= 9
Question 15
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If the roots of the quadratic equation ax² + bx + c = 0 are real and equal, then ______.

A
b² – 4ac = 0

B
b² – 4ac + ab > 0

C
b² – 4ac + 2a = 0

D
b² – 4ac < 0

Solution

ax² + bx + c = 0 for equal and real D = 0
D = b² - 4ac = 0
Question 16
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Which of the following equations can be obtained after completing the square of x²+ 6x + 3 = 0?

A
(x + 1)² = 5

B
(x + 3)² = 6

C
(x - 2)² = 9

D
(x - 4)² = 7

Solution

x² + 6x + 3 = 0
(x + 3)² + 3 - 9 = 0
(x + 3)² = 6
Question 17
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What will be the discriminant of the given quadratic equation?

ax² + bx + c = 0

A
b² – 4a²c

B
b² + 2ab

C
b² – 4ac

D
b² + 4a²

Solution

ax² + bx + c = 0
b² – 4ac
Question 18
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Which of the following equations has no real roots?

A
x² + x + 12 = 0

B
x² - x - 1 = 0

C
2x² + 7x + 5 = 0

D
x² + x - 1 = 0

Solution

x² + x + 12 = 0
D = 1 - 4 x (12)
= - 47

D < 0
Hence no real root.
Question 19
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Which of the following equations can be obtained after completing the square of x² + 4x + 2 = 0?

A
(x + 3)² = 6

B
(x - 2)² = 4

C
(x - 3)² = 2

D
(x + 2)² = 2

Solution

x² + 4x + 2 = 0
(x + 2)² + 2 - 4 = 0
(x + 2)² = 2
Question 20
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Which of the following equations has 2as one of its solutions?

A
(2x + 4)² = 3

B
(x - 2)² = 0

C
(2x + 2)² = 9

D
None of these

Solution

(x - 2)² = 0
x = 2 satisfy this
Question 21
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Which of the following equations can be obtained after completing the square of x² + 9x + 7 = 0?

A
=

B
(2x + 9)² =

C

D
=

Solution

x² + 9x + 7 = 0
= 0
Question 22
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Which of the following equations has real and distinct roots?

A
x² - 5x + 5 = 0

B
2x² - 12x + 2 = 0

C
2x² + 5x + 1 = 0

D
All of the above

Solution

For real and distinct roots
D = b² - 4ac > 0
(1) 25 - 20 > 0 Real and distinct roots
(2) 144 - 16 > 0 Real and distinct roots
(3) 25 - 8 > 0 Real and distinct roots
All of the above
Question 23
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Which of the following equations has as one of its solutions?

A
(3x + 4)² = 64

B
(2x - 3)² = 49

C
(4x - 3)² = 81

D
(2x + 3)² = 100

Solution

(2x + 3)² = 100
= 100
(7 + 3)² = 100
(10)² = 100
100 = 100
Question 24
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Which of the following equations can be obtained after completing the square of x² + 4x - 1 = 0?

A
(x + 2)² = 4

B
(x - 2)² = 5

C
(x + 2)² = 5

D
(x - 2)² = 4

Solution

x² + 4x - 1 = 0
(x +2)² - 1 - 4 = 0
(x + 2)² = 5
Question 25
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If the quadratic equation ax² + bx + c = 0 has no real roots, then ______.

A
b² - 4ac < 0

B
b² - 2a² > 0

C
b² - 2ab = 0

D
b² - 2ab > 0

Solution

b² - 4ac < 0
Question 26
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What will be the discriminant of the given quadratic equation?
x² + 7x - 1 = 0

A
53

B
50

C
49

D
48

Solution

x² + 7x - 1 = 0
D = 49 - 4 (1) (- 1)
= 53
Question 27
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Which of the following equations can be obtained after completing the square of x² - 10x + 5 = 0?

A
(x + 6)² = 18

B
(x + 4)² = 16

C
(x - 5)² = 20

D
(x + 3)² = 15

Solution

x² - 10x + 5 = 0
(x - 5)² + 5 - 25 = 0
(x - 5)² = 20
Question 28
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Which of the following equations has real and distinct roots?

A
6x² - 2x + 5 = 0

B
2x² - 7x + 19 = 0

C
4x² - 12x + 9 = 0

D
5x² - 11x - 12 = 0

Solution

5x² - 11x - 12 = 0
D = 121 - 4 (5) (- 12)
= 121 + 240 = 361 > 0
Hence real and distinct roots
Question 29
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Which of the following equations has -1 as one of its solutions?

A
(x + 5)² = 16

B
(2x + 1)² = 24

C
(x - 1)² = 0

D
(x + 7)² = 39

Solution

(x + 5)² = 10
x = - 1 satisfy this
(- 1 + 5)² = 4² = 16
Question 30
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Which of the following equations can be obtained after completing the square of 3x² + 4x - 1 = 0?

A
(3x - 2)²= 7

B
(3x + 2)² = 7

C
(3x + 4)² = 7

D
(3x - 4)² = 7

Solution

3x² + 4x - 1 = 0
x² + x - = 0
= 0

(3x + 2)² = 7
Question 31
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Which of the following quadratic equations has 0 as discriminant?

A
x² + 4x + 2 = 0

B
x² + 4x + 4 = 0

C
2x² + x - 1 = 0

D
None of these

Solution

x² + 4x + 4 = 0
D = 16 - 4 x 4
= 16 - 16 = 0
Question 32
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Which of the following equations has 8 as one of its solutions?

A
(5x - 4)² = 80

B
(2x - 5)² = 121

C
(3x + 7)² = 50

D
(7x - 3)² = 35

Solution

(2x - 5)² = 121
x = 8 satisfies this
(2 x 8 - 5)² = (16 - 5)² = 11² = 121
Question 33
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Which of the following equations has no real roots?

A
7x² - 3x + 5 = 0

B
9x² + 11x - 3 = 0

C
9x² - 30x + 25 = 0

D
8x² - 16x + 1 = 0

Solution

7x² - 3x + 5 = 0
D = 9 - 140
= - 131 hence no real roots.
Question 34
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Which of the following equations can be obtained after completing the square of 3x² - 11x - 4 = 0?

A

B

C

D

Solution

3x² - 11x - 4 = 0
x² - x - = 0
= 0
Question 35
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Which of the following equations has 56 as discriminant?

A
2x² + 4x + 7 = 0

B
x² + 8x - 2 = 0

C
2x² + 8x + 1 = 0

D
2x² + 16x - 27 = 0

Solution

(1) D = 16 - 56 = - 40
(2) D = 64 + 8 = 72
(3) = 64 - 8 = 56
Question 36
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Which of the following equations has -as one of its solutions?

A
(x +)² = 2

B
(x - 2)² = 18

C
(x -)² = 0

D
(x - 1)² = 2

Solution

-as a solution?
(x - 2)² = 18
(-)²
(- 3)²
9 x 2 = 18
Question 37
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Which of the following equations has equal roots?

A
x² + 4x + 4 = 0

B
x² + 5x + 5 = 0

C
x² + x + 1 = 0

D
x² + 6x + 6 = 0

Solution

x² + 4x + 4 = 0
D = 16 - 16 = 0 has equal roots.
Question 38
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Which of the following equations can be obtained after completing the square of 2x² - 3x + 1 = 0?

A

B

C

D

Solution

2x² - 3x + 1 = 0
x² - = 0
= 0
Question 39
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What will be the discriminant of the given quadratic equation?
x² + x + 1 = 2

A
5

B
4

C
- 4

D
- 5

Solution

x² + x + 1 = 2
x² + x - 1 = 0
D = 1 - 4 (- 1)
= 5
Question 40
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Which of the following equations can be obtained after completing the square of 3x² + 7x + 2 = 0?

A

B

C

D

Solution

3x² + 7x + 2 = 0
x² + = 0
= 0