# numpy.roots

numpy.roots(p)

  Return the roots of a polynomial with coefficients given in p.

  Note

  This forms part of the old polynomial API. Since version 1.4, the new polynomial API defined in `numpy.polynomial` is preferred. A summary of the differences can be found in the transition guide.

  The values in the rank-1 array p are coefficients of a polynomial. If the length of p is n+1 then the polynomial is described by:

      p[0] * x**n + p[1] * x**(n-1) + ... + p[n-1]*x + p[n]

  Parameters
    p array_like

      Rank-1 array of polynomial coefficients.

  Returns
    out ndarray

      An array containing the roots of the polynomial.

  Raises
    ValueError

      When p cannot be converted to a rank-1 array.

  See also

  `poly`

    Find the coefficients of a polynomial with a given sequence of roots.

  `polyval`

    Compute polynomial values.

  `polyfit`

    Least squares polynomial fit.

  `poly1d`

    A one-dimensional polynomial class.

  Notes

  The algorithm relies on computing the eigenvalues of the companion matrix [1].

  References

  1

    R. A. Horn & C. R. Johnson, Matrix Analysis. Cambridge, UK: Cambridge University Press, 1999, pp. 146-7.

  Examples

      >>> coeff = [3.2, 2, 1]
      >>> np.roots(coeff)
      array([-0.3125+0.46351241j, -0.3125-0.46351241j])

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