SOLUTION: Find the range of values of K for which the line {{{y+kx+9=0}}} does not intersect the curve {{{y=(x)^(2)-2x}}} *Please answer as soon as possible bro =)

Algebra ->  Coordinate-system -> SOLUTION: Find the range of values of K for which the line {{{y+kx+9=0}}} does not intersect the curve {{{y=(x)^(2)-2x}}} *Please answer as soon as possible bro =)      Log On


   

Question 465569: Find the range of values of K for which the line y%2Bkx%2B9=0 does not intersect the curve y=%28x%29%5E%282%29-2x
*Please answer as soon as possible bro =)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
You have to have -kx+-+9+=+x%5E2+-+2x
<==> x%5E2+%2B+%28k%2B2%29x+%2B+9+=+0
For non-intersection, the discriminant should be < 0.
Whence %28k-2%29%5E2+-+4%2A1%2A9+%3C0
==> k%5E2+-+4k+-+32+%3C0
<==> (k-8)(k + 4) < 0 ==> the solution set is the interval (-4,8)
Hence as long as kepsilon%28-4%2C8%29, the line and the parabola won't intersect.