Solved Examples and Worksheet for No real Solutions for Quadratic Equations

Q1Solve : x2 + 64 = 0
A. ± 8i
B. ± 8
C. Only 8i

Solutions
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Step: 1
x2 + 64 = 0
Step: 2
x2 = - 64
  [Subtracting 64 from the two sides of the equation.]
Step: 3
x = ± (-64)
  [Find the square root of both sides.]
Step: 4
x = ± 64i2
  [i2 = - 1.]
Step: 5
x = ± 8i
Step: 6
The values of x that satisfy the given equation are 8i and - 8i.
Correct Answer is :   ± 8i
Q2Solve.
13x2 + 16 = 0
A. ±(413)i
B. ± (413)i
C. ± i13
D. None of the above

Solutions
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Step: 1
13x2 + 16 = 0
Step: 2
13x2 = - 16
  [Subtracting 1 from the two sides of the equation.]
Step: 3
x2 = - 1613
  [Divide throughout by 2.]
Step: 4
x = ± (- 1613)
  [Find the square root of both sides.]
Step: 5
x = ± (1613)i2
  [i2 = - 1.]
Step: 6
x = ± 1613 i = ± (413i)
Step: 7
The values of x that satisfy the given equation are (413i) and - (413)i.
Correct Answer is :    ±(413)i
Q3Solve: x2 + 4 = - 64

A. ± i64
B. ± 64
C. ± 4
D. ± i68

Solutions
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Step: 1
x2 + 4 = - 64
Step: 2
x2 = - 68
  [Subtracting 4 from the two sides of the equation.]
Step: 3
x = ±(-68)
  [Find the square root of both sides.]
Step: 4
x = ± 68i2
  [i2 = - 1.]
Step: 5
x = ± i68
Step: 6
The values of x satisfying the given equation are i68 and - i68.
Correct Answer is :   ± i68
Q4Solve: 6x2 + 1 = x2 - 4
A. 0.83
B. - 1
C. ± i
D. 0

Solutions
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Step: 1
6x2 + 1 = x2 - 4
Step: 2
6x2 - x2 = - 4 - 1
  [Group the like terms and simplify.]
Step: 3
5x2 = - 5
  [Simplify.]
Step: 4
x2 = - 1
  [Divide by 5 on both sides.]
Step: 5
x = ± - 1
  [Find the square root of both sides.]
Step: 6
x = ± i2
  [i2 = - 1.]
Step: 7
x = ± i
Step: 8
The values of x that satisfy the given equation are i and - i.
Correct Answer is :    ± i
Q5Solve: x2 + 25 = - 4
A. ± i4
B. ± 25
C. ± 4
D. ± i29

Solutions
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Step: 1
x2 + 25 = - 4
Step: 2
x2 = - 29
  [Subtracting 25 from the two sides of the equation.]
Step: 3
x = ±(-29)
  [Find the square root of both sides.]
Step: 4
x = ± 29i2
  [i2 = - 1.]
Step: 5
x = ± i29
Step: 6
The values of x satisfying the given equation are i29 and - i29.
Correct Answer is :   ± i29
Q6Solve: 5x2 + 1 = x2 - 3

A. 0.83
B. ± i
C. 0
D. - 1

Solutions
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Step: 1
5x2 + 1 = x2 - 3
Step: 2
5x2 - x2 = - 3 - 1
  [Group the like terms and simplify.]
Step: 3
4x2 = - 4
  [Simplify.]
Step: 4
x2 = - 1
  [Divide by 4 on both sides.]
Step: 5
x = ± - 1
  [Find the square root of both sides.]
Step: 6
x = ± i2
  [i2 = - 1.]
Step: 7
x = ± i
Step: 8
The values of x that satisfy the given equation are i and - i.
Correct Answer is :    ± i
Q7Solve: x2 = - 16
A. 1 + 4i
B. ± 2i
C. ±4i
D. ± 4i

Solutions
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Step: 1
x2 = - 16
  [Original equation.]
Step: 2
x = ±  -16
  [Find the square root of both sides.]
Step: 3
x = ± 16i 2
  [i2 = - 1.]
Step: 4
x = ± 4i
Step: 5
The values of x satisfying the given equation are 4i and - 4i
Correct Answer is :   ± 4i
Q8Solve: x2 + 40 = - 9

A. 7i
B. ± 17i
C. - 7i
D. ± 7i

Solutions
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Step: 1
x2 + 40 = - 9
Step: 2
x2 = - 49
  [Subtracting 40 from the two sides of the equation.]
Step: 3
x = ±(- 49)
  [Find the square root of both sides.]
Step: 4
x = ± 49i2
  [i2 = - 1.]
Step: 5
x = ± i49
Step: 6
x = ± 7i
Step: 7
The values of x satisfying the given equation are 7i and - 7i.
Correct Answer is :   ± 7i
Q9Solve: x2 + 98 = 49

A. 7i
B. - 7i
C. ± 7i
D. 17i

Solutions
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Step: 1
x2 + 98 = 49
Step: 2
x2 = 49 - 98 = - 49
  [Subtracting 96 from the two sides of the equation.]
Step: 3
x = ± - 49
  [Find the square root of both sides.]
Step: 4
x = ± 49i2
  [i2 = - 1.]
Step: 5
x = ± 7i
Step: 6
The values of x that satisfy the given equation are 7i and - 7i.
Correct Answer is :   ± 7i
Q10Solve: 4x2 = - 4
A. - 1
B. 0
C. ± i
D. 1

Solutions
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Step: 1
4x2= - 4
Step: 2
x2 = - 1
  [Divide by 4 on both sides.]
Step: 3
x = ± - 1
  [Find the square root of both sides.]
Step: 4
x = ± i2
  [i2 = - 1.]
Step: 5
x = ± i
Step: 6
The values of x that satisfy the given equation are i and - i.
Correct Answer is :   ± i

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