Question

For what values of k will the equation 4x² + 8x + k = 0 have two complex solutions?

Answer 1

k > 4

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

Answer 2

k = -4x² - 8x

Explanation:

Subtract 4x² from both sides of the equation.

8x + k = -4x²

Subtract 8x from both sides of the equation.

k = -4x² - 8x