solve roots of nth root polynomial

import numpy as np

def characteristic_matrix(coeffs):
    n = coeffs.size-1
    A = np.eye(n, k=1);

    print -(1/coeffs[0]) * coeffs[-1:0:-1]
    A[-1,::] = -1 * (coeffs[-1:0:-1]/coeffs[0])
    return A

def get_real_roots(coeffs):
    A=characteristic_matrix(coeffs)
    print A
    start = time.time()
    E,Q=np.linalg.eig(A)
    end = time.time()

    print "Solved in:"
    print end-start

    return E

get_real_roots(np.array([-3.0, 0.0, 5.0, -1.0, 0.0])