The polynomial is expressed as a dot product, and the exponential function 
is also expressed as a dot product.  These are used to find the normal in 
the direction of the solution, by selecting a point not on the plane defined 
by the two vectors.  Their components are the coefficients of the polynomial 
and the expansion of th exponential function.

After an algebraic division, the remainder is expanded as a Maclaurin series 
to 3 degrees, and the roots become the solutions to a cubic.

http://mypeoplepc.com/members/jon8338/polynomial/