A polynomial is the dot product of the normal to a plane and a space curve.

Wherever the curve intersects the plane there is a solution.

The plane intersects the axes at different points, and the lines adjoining

two intercepts form a basis. With the bases we can construct the position

where the curve intersects the plane and therefore arrive at the solutions.

This starts out finding 7th degree roots, starts a Geometric Series and then

changes to finding the roots to the 6th degree. Finally I took a stab at

the quartic.

http://www.stonetabernacle.com/poly...roots.html
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