^

Solve,

a_0*x^0 + a_1*x^1 + a_2*x^2 + ... +a_n*x^n = 0

x = ?

Let

Q=(a_0,a_1,a_2,...,a_n)
U=(1,1,1,...,1)
E=(1,1,1/2!,1/3!,1/4!,...,1/n!)
P=(1,x,x^2,x^3,....,x^n)

u=U/|U|

by vector analysis,

P*u=|Q|^2(E*P)/[(E*Q)(Q*u)]

express P as ratios of Q,U,E

qQ+rU+sE=P

dot both sides by Q,u,E and note that P*E=e^x.
Solve the matrix,

Q*Q  Q*U  Q*E  | 0
Q*u  U*u  E*u  | {|Q|^2/[(E*Q)(Q*u)]}e^x
Q*E  E*U  E*E  | e^x

P/|P| = (s_0,s_1,s_2...)  e^x cancels

P=P_u/s_0 because x^0=1

P=(p_0,p_1,p_2,p_3,...,p_n)=(1,x,x^2,x^3,..,x^n)

x=a+bi

(a+bi)^(1/n)
=
{a^2+b^2}^(.5/n)[cos((arctan(b/a)/n)] real
+{a^2+b^2}^(.5/n)[sin((arctan(b/a)/n)]i complex

by DeMoirve

x_n+1=x_n-
(a_0+a_1*x+a_2*x^2+a_3*x^3+...+a_n*x^n)
/
(a_1+2*a_2*x+3*a_3*x^2+...+n*a_n*x^(n-1)  )

by Newton

This strategy has some flaws.  You need n vectors to construct n
dimensions, 
but I only used 3.  Also, it is only useful for large n in order to
reflect 
the contribution from E*U=e^x.  It also generates numbers too large for 
computing.

Its advantage is that it does produce some numbers to play around with 
Newton's Method.  Their initial values may or may not be accurate, but
after 
7 iterations and 50 repeats, does it really matter?

=(a_1+MMULT(s_2*TRANSPOSE(qd_2)*((r_iter_7d*TRANSPOSE(s_2))^TRANSPOSE(n_1_2))*COS(ang_iter_7d*TRANSPOSE(n_1_2)),n_2))