Math inequality question

I mentioned inequality because th question is listed under the inequality lesson in my text.

Question is:
Find the values of k for which kx^2 + 8x + 5 = 0

I'm not sure where to start with this one. Please provide steps and proper explanation as I want to untderstand it.

Thanks in advance :)

The equation has roots for any arbitrary value of k that you care to choose. To limit the possible values of k, you have to specify additional conditions. For example, for what values of k are the roots of the equation real valued?

kx² + 8x + 5 = 0
x = [-8±√(64-4*5*k)]/(2k)
x is real valued if 64-20k ≥ 0
20k ≤ 64
k ≤ 16/5 (3.2, not 3.5)

if k ≤ 16/5, the roots of the equation are real valued and the curve intersects or is tangent to the x-axis. Otherwise the roots are complex valued and the curve has no x-intercepts.

Figured it out~ Except, so did someone else LOL
Oh well; post anyway, since I did it already :P

Calculations:
http://i1097.photobucket.com/albums/g346/Shei431/Images/find_k.jpg

Agreed with person above; it's 3.2 not 3.5

Discriminant (b^2-4ac) >=0
64-20k>=0
k<=16/5
k<=3.2

k has to be 3.
3x^2 + 8x + 5 = 0
(3x + 5)(x + 1) = 0