If equation 2x² + 6(k + 3)x - 9k=0 has equal roots, the possible values of k do not exist
How to determine the possible values of k
From the question, we have the following parameters that can be used in our computation:
2x² + 6(k + 3)x - 9k = 0
The equation has equal roots
This means that
b² = 4ac
Where
a = 2
b = 6(k + 3)
c = -9k
using the above as a guide, we have the following:
[6(k + 3)]² = 4 * 2 * -9k
36(k² + 6k + 9) = -72k
Divide both sides by 36
k² + 6k + 9 = -2k
So, we have
k² + 8k + 9 = 0
Expand
k² + 8k + 9 = 0
The equation is not factorizable
Hence, there is no solution for k