I personally think the criticism of Hoosie's post#5 has been overly harsh.
I agree that posts #4, #6 and #8 are the best and fastest way to let most people find the answer. But given that OP had stopped posting their previously quick responses then I think it was very reasonable for Hoosie to try a different approach. (In all likelihood the OP had understood at post#4 and had simply gone away)
I might be a bit biased because I have a very visual memory! I like the idea of illustrating graphically the one-to-one relationship between x-axis crossings and the individual factors of a polynomial (not just a quadratic). It is easy to see the polynomial is not zero between any of the factors. This is less direct then post #8, but it might be a powerful illustration for some people - BUT ONLY while learning (I'm certainly not suggesting a graph should be done every time!)
Cubist and Hoosie
I should have said in post # 6 "makes no pedagogic sense." Leaving out the word "pedagogic" may have contributed to an overly harsh tone, and for that I apologize. Nevertheless, I want to clarify the pedagogic point that I was trying to make.
If you are asked whether a is a root of f(x), the
general method to determine that question is to see whether f(a) = 0. It is general because it derives
directly from the definition of "root." So to focus on the specific facts about this function, namely that it is a quadratic and that therefore its graph is a parabola with at most two x intercepts, completely loses sight of the general lessons that this problem could teach, namely to pay close attention to definitions and to learn general methods that will apply to whole classes of problems.
Now I agree that if you have a graphing calculator to hand, it may just as easy to determine the roots of a specific function as to calculate the value of that function at a given point. But to use the graph to do that, you still have to grasp the definition of root. That crystal clear focus on definitions was, for me at least, the brilliance of SK's answer, and, to all appearances, the OP got that message virtually instantaneously. To have a later post say, "it may make more sense" to graph than to understand a definition when the graph will help only if you already understand the definition really does make no pedagogic sense to me.
Now, in a later post, hoosie has said that he intended it as a method for checking the answer suggested by SK. Obviously, I have no objection to checking answers. Nor do I have any objection whatsoever to reinforcing an idea by visual means. What I originally objected to was the apparent failure to see that any method for solving the specific problem depended on understanding the general definition of root and that that understanding gives rise to a conceptually obvious way to solve any problem of this kind.