Question

Find the set of values of k for which the y = kx – 4 intersects the curve of y = x2 – 2x at two distinct points.

Answer 1

Answer:

For ax^2+bx+c=0,

x^2+x(-2-k)+4=0,

So, b=-2-k,

a=1, c=4, so

(-2-k)^2-(4*1*4)>0,

4+4k+k^2-16>0,

k*2+4k-12>0,

(k+6)*(k-2)>0,

the points of interest are

k=-6, k=2, so

look at k<-6, -6<k<2, and

k>2.

Just plug in values for each

interval and you will see

that k<-6 and k>2.