Expert: David Hemmer - 10/7/2008

Question
hey there would really appreciate if you could help me out. the question is: Determine the value of k if the graph of y=2x^2-2x+3k intersects the x-axis at two distinct points?

Answer
The x axis is y=0. If you look at the quadratic formula you see a plus or minus the square root of b^2-4ac. So when b^2-4ac is postive there are two distinct real roots.

If your example b^2-4ac=4-24k

So you need 4-24k>0, or 1/6>k.

So for any value of k less than 1/6 you get two points of intersection.