Describe the issue:

Description

When I define a polynomial with a single very large root (and other small ones), I get a significant difference between the outcomes of the roots and polyroots functions. Mainly the small roots seem to differ. Maybe even more importantly, the outcomes can also become complex in the polyroots function.

Reproduce the code example:

from numpy import roots, sort, array
from numpy.polynomial.polynomial import polyroots

p = array([0.5, -0.2, -5e+15, 0.04])
print(f'roots:     {sort(roots(p[::-1]))}') # [-1.00000000e-08  9.99999998e-09  1.25000000e+17] 
print(f'polyroots: {sort(polyroots(p))}')   # [-7.50602596e-09  7.50602647e-09  1.25000000e+17]

print()

p = array([0.5, -0.2, -5e+15, 0.05])
print(f'roots:     {sort(roots(p[::-1]))}')  # [-1.00000000e-08  9.99999998e-09  1.00000000e+17]
print(f'polyroots: {sort(polyroots(p))}') # [1.68735664e-16-2.94078821e-09j 1.68735664e-16+2.94078821e-09j ...]

Error message:

No response

Python and NumPy Versions:

• Numpy version: 2.1.3
• Python version: 3.13.0
• Platform: MacOS 15.1.1

Runtime Environment:

No response

Context for the issue:

I'm not 100% sure this can be considered a bug, apologies if this is not the case. The reason for reporting is that as a naive user, I expect 'new' API's to behave identical (or at least similar) to the original functions. I'm using these functions to find the intersections of 2 polynomials, which represent the performance characteristics of a propeller.

As far as I'm concerned, this issue does not need to be prioritised in any way. I just wanted to make sure that this behaviour is known if this wasn't already the case. Thanks either way for your input/help!