Expert: Richard J. Raridon - 4/12/2010

Question
Hi, I'm a Gr12 home student, currently busy revising past exam papers,I'm struggling with the following question and can't find the method anywhere in my textbooks, even after looking at the answer I still can't determine the method being used, the answer to the question below is 0<k>2

Given: f(x) = 1/2x(x+4)
[2.1.2. Draw the sketch graph of F, I did this correctly,
x-intercepts = 0 and 2, y-intercept= 0, turning point= (-2;2)]

QUESTION 2.1.4
USE THE GRAPH OF QUESTION 2.1.2 to determine the values of K for
which -x(x+4)=2k has two unequal roots.

Answer
You can find K without referring to the graph.  If you multiply out that expression and rearrange, you have x^2 +4x +2K = 0 so x = [-4+/-(16-8K)^1/2]/2 and you get two real roots if (16-8K) is greater than zero.  Therefore K has to be less than 2 but I don't see why it has be be greater than zero since negative values of K will work