[VA] SRC #012b - Then and Now: Root

[J-F Garnier]

I was not sure to fully understand the problem. Do you have to search for the smallest (in absolute value) root in the real or complex domain?
When we are speaking of roots of a polynomial, we are often referring to its complex roots.
But when I read 'absolute value', I tend to link it to a real number, even if the ABS function is often used in HP programming languages to calculate the norm or modulus of a complex number.

So I will assume that we are looking for real roots.
My first thoughts: a real root must be negative, and greater than -1 since the polynomial quickly takes very large values for |X|>1.

My first analysis (using HP calculators), cutting the polynomial to the first 10-100 terms seemed to indicate me that there is no real root.
So if there are real roots, they are close to -1, otherwise the higher X^i terms would be negligible and I would have found the root with the truncated polynomial.
I will try to build a program to support this, but I'm not sure I will be able to propose something useful, even on a fast emulator.

J-F