Originally Posted by

**Archie** 1) and 2), set (for example) $y=x+k$, the roots of the quadratic in $y$ are those of the roots of the first quadratic in the question. Replace $y$ with the expression for $x$ and you have your result.

3) is similar: $y = nx$. 4) is a special case of 3).

In 5) "inverse" presumably means "reciprocal". Set $y = \frac1x$ and form a quadratic from the resultant equation.

6) requires something mildly different, but it ought to be pretty clear how to approach it from what I've already written.