Find the set of values of k for which the line y=kx-4 intersects the curve y=x²-2x at 2 distinct points?

Step-by-step explanation:

Given

Required

Possible values of k

The general quadratic equation is:

Subtract and

Factorize:

Rewrite as:

Compare the above equation to:

For the equation to have two distinct solution, the following must be true:

So, we have:

Expand

Rewrite as:

Expand

Factorize

Factor out k + 6

Split:

or

So:

or k

To make the above inequality true, we set:

or

So, the set of values of k is: