# polyroot: Find Zeros of a Real or Complex Polynomial

## Description

Find zeros of a real or complex polynomial.

## Usage

 `1` ```polyroot(z) ```

## Arguments

 `z` the vector of polynomial coefficients in increasing order.

## Details

A polynomial of degree n - 1,

p(x) = z1 + z2 * x + … + z[n] * x^(n-1)

is given by its coefficient vector `z[1:n]`. `polyroot` returns the n-1 complex zeros of p(x) using the Jenkins-Traub algorithm.

If the coefficient vector `z` has zeroes for the highest powers, these are discarded.

There is no maximum degree, but numerical stability may be an issue for all but low-degree polynomials.

## Value

A complex vector of length n - 1, where n is the position of the largest non-zero element of `z`.

## Source

C translation by Ross Ihaka of Fortran code in the reference, with modifications by the R Core Team.

## References

Jenkins, M. A. and Traub, J. F. (1972). Algorithm 419: zeros of a complex polynomial. Communications of the ACM, 15(2), 97–99. \Sexpr[results=rd,stage=build]{tools:::Rd_expr_doi("10.1145/361254.361262")}.

`uniroot` for numerical root finding of arbitrary functions; `complex` and the `zero` example in the demos directory.
 ```1 2 3 4``` ```polyroot(c(1, 2, 1)) round(polyroot(choose(8, 0:8)), 11) # guess what! for (n1 in 1:4) print(polyroot(1:n1), digits = 4) polyroot(c(1, 2, 1, 0, 0)) # same as the first ```