You must solve the following for K.
If someone has made a genuine attempt at a problem, I don't see how helping them obtain an answer is detrimental. That way they are able to complete the other homework problems, which are more than likely similar to the one asked. If they have multiple questions, show how to complete one and let them solve the others. Then, they can show what they learned and can post their solutions to see if they are correct. Or, at the least, providing an obvious hint that that leads to the solution.
When a person asks a question say on ODE's and I answer it, I do not do it fully because since I know the user needs to be already familar with some concepts and I skip steps and sometimes show the final equation but do not complete it (again because I am lazy).
But I do not think it is helpful when somebody asks how to do a certain differenciation and somebody posts, ..."Use the chain rule". Such a post is a totally useless posts that does not help the reader at all.
Just using my psychic powers.
In any case I suspect further explanation is needed
The discriminant is
When a quadratic has no real roots then
Substitute these values into the inequality to get the quadratic inequality
that Plato got. You must solve this (by sketching the graph of to help)
I've got the impression that you and your problem are little bit out of sight.
So let's start again.
1. You've got a quadratic equation in x. I presume that you know that you have to use a special formula to solve this equation:
If the equation is: , then the solutions are:
2. Compare the given equation with the standard equation. You'll find out:
a = K
b = -4
C = 5-K
Now plug in these terms into the formula and you'll get:
The radicand must be zero or positive (That means greater than zero) to get real values for x. (The radicand is called the dicriminant because it separates the solution into real or complex values)
3. So you have to calculate the values of K so that the dicriminant is zero or positive.
. Expand the LHS of the inequality:
. Divide by 4
4. Now you have a product which is gerater or equal zero. A prduct of two factors is positive if both factors have the same sign (More colloquial: +*+ = + or -*-= +). "+" means greater as zero, "-" menas smaller than zero.
So you get:
I'll leave these inequalities for you.