Quadratic equations ..

Question

The set of non-zero values of k such that the equation $|x^2-10x+9| =kx$ is satisfied by atleast one and atmost three values of x, lies in ___.

The answer is $(-\infty, -16] \cup [4 , \infty) $.

How do you get that ?

Answer 1

Hints:

1. Note that $|y|=kx$ iff $kx>0$ and $y=kx$ or $y=-kx$.
2. Using the previous hint, write down the two cases in consideration and isolate all the terms to one side so that the other side is $0$.
3. For each case, set the discriminant to be non-negative and solve.