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5 votes
5 votes
select all the functions that have no real number solution
4x ^(2) + 100 = 0
3x ^(2) - 9 = 0
x ^(2) + 1 = 0
6x ^(2) - 216 = 0

User Mike Barlotta
by
3.0k points

1 Answer

22 votes
22 votes

Answer

Options A and C have no real number solution

Step-by-step explanation

To know which equations have no real number solutions, we will need to try to solve each of the equations

Option A

4x² + 100 = 0

4x² = -100

Divide both sides by 4

(4x²/4) = (-100/4)

x² = -25

We now take the square root of both sides

√x² = √(-25)

x = √(-25)

Since the square root of any number is a complex number,

x = ±5i

The answer is not a real number solution

Option B

3x² - 9 = 0

3x² = 9

Divide both sides by 3

(3x²/3) = (9/3)

x² = 3

We now take the square root of both sides

√x² = √3

x = ±√3

This is a real number solution.

Option C

x² + 1 = 0

x² = -1

We now take the square root of both sides

√x² = √(-1)

x = √(-1)

Since the square root of any number is a complex number,

x = ±i

The answer is not a real number solution

Option D

6x² - 216 = 0

6x² = 216

Divide both sides by 6

(6x²/6) = (216/6)

x² = 36

We now take the square root of both sides

√x² = √(36)

x = √(36)

x = ±6

The answer is a real number solution

Hope this Helps!!!

User Jarod Elliott
by
2.6k points