[R] polyroot behaviour

[Deepayan Sarkar]

How can an odd degree polynomial be positive for all x?


Deepayan

On Thu, 2 Oct, 2025, 6:14 pm tgs77m--- via R-help, <r-help using r-project.org>
wrote:

> Colleagues,
>
> g <- function(x) ( x^11 + 1000*x^10 + 500 *x^9 + 1 )
> coeffs <- c(1, rep(0, 8), 500, 1000, 1)
> roots <- polyroot(coeffs)
>
> Output
>
> [1]    0.25770068+3.958197e-01i
>  [2]   -0.34615184+3.782848e-01i
>  [3]   -0.04089779-4.838134e-01i
>  [4]    0.44124314-1.517731e-01i
>  [5]   -0.04089779+4.838134e-01i
>  [6]   -0.56201931-1.282822e-01i
>  [7]   -0.34615184-3.782848e-01i
>  [8]    0.44124314+1.517731e-01i
>  [9]   -0.56201931+1.282822e-01i
> [10]    0.25770068-3.958197e-01i
> [11] -999.49974975+1.110223e-16i
>
> [11] -999.49974975+1.110223e-16i  makes  no sense since f>0 for all x
>
> Why does polyroot do this?
>
> Thomas Subia
>
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