Transform a polynomial so that positive roots are shifted right and negative roots are shifted left I'm trying to figure out if it is possible to shift the roots of a polynomial outward, instead of to the left or right.  Its relatively simple to shift all the solutions in one direction by substituting (x-k) or (x+k) for x within the equation, but is it possible to shift all the positive solutions to the right and all the negative solutions to the left?  

You can scale the polynomial.
For instance, if $r$ is a root of $p(x)$, then $2r$ is a root of $p(x/2)$, which shifts positive right and negative left (and imaginary more along the corresponding direction).
