In his book, The Annotated Turing, Charles Petzold says (emphasis mine),
Using a straightedge and compass to construct geometrical shapes is equivalent to solving certain forms of algebraic equations.
Does that mean that given any polynomial $p(x)$ in one variable $x$, an algorithm can be written to do the construction of a geometric shape whose equation is $p(x) = 0$ (algebraic equation) using a straightedge and compass?
And what does he mean by certain forms of algebraic equations? Is he referring only to polynomials with real roots?