Hi there!
We can use discriminants to determine the value of k for which the equation would have complex solutions. (Those involving i)
If b² - 4ac < 0, then the equation will have complex solutions. Therefore:
Plug in the given values of b and a to solve:
7² - 4(2)(k) < 0
Simplify:
49 - 8k < 0
Solve the inequality:
49 < 8k
6.125 < k
k > 6.125. Anything greater than 6.125 would result in complex solutions.