Quadratic Functions, Equations and Inequalities

Consider \(\frac{x^2-k}{x-2}=3,\) where \(k\) is a constant.

1. Find \(k\) so that \(x=2\) is a root of the equation obtained after clearing the denominator. For that value of \(k\), solve the original equation.

2. Find \(k\) so that \(x=0\) is a valid root. Find the other valid root.