Answer:
k > 4
Step-by-step explanation:
Using the discriminant to determine the nature of the solutions
• If b² - 4ac < 0 then the solutions are not real, that is they are complex
Given
4x² + 8x + k = 0
with a = 4, b = 8, c = k , then
8² - (4 × 4 × k) < 0
64 - 16k < 0 ( subtract 64 from both sides )
- 16k < - 64
Divide both sides by - 16, reversing the symbol as a result of dividing by a negative quantity.
k > 4
Any value of k greater than 4 will mean the equation has 2 complex solutions
