Question 28934
There's a mistake in this question.
As you found out, you will end up with complex roots.
That's the problem!
You can't compare complex numbers. Unless they are both totally real or totally imaginary.
You can't have an inequality such as 3 < 2i, or even 2 + 5i > 1 - 3i.
You can test this out by graphing the curve of (1/2)x² + 3x and see where its lowest point is wrt the line y = -6.
{{{ graph( 300, 200, -8, 5, -7, 3, x^2/2+3x, -6) }}}
As you can see, the line y = -6 is less than the curve (1/2)x² + 3x at all times, so that inequality never holds.