Answer
Options A and C have no real number solution
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!!!
