I know Graeffe's method to approximate roots is great, but people always find troubles when they convert the root in n-th-root form into base 10 form by hand, for example, a large number in 64-th-root.
What is a more modern way of getting numerical solution/roots of polynomial in base 10 than this by hand? I prefer a method that you could control the accuracy in terms of significant digit
Graeffe's method - http://mat.iitm.ac.in/home/sryedida/public_html/caimna/transcendental/polynomial%20methods/direct.html
Now a bounty is offered to address all the concerns.