  Peculiarities of obtaining parameters for broad multi-channel resonances from
data are discussed analyzing the experimental data on processes
$\pi\pi\to\pi\pi,K\bar{K}$ in the $I^GJ^{PC}=0^+0^{++}$ channel in a
model-independent approach based on analyticity and unitarity and using an
uniformization procedure. We show that it is possible to obtain a good
description of the $\pi\pi$ scattering data from the threshold to 1.89 GeV with
parameters of resonances cited in the PDG tables as preferred. However, in this
case, first, representation of the $\pi\pi$ background is unsatisfactory;
second, the data on the coupled process $\pi\pi\to K\bar{K}$ are not well
described even qualitatively above 1.15 GeV when using the resonance parameters
from the only $\pi\pi$ scattering analysis. The combined analysis of these
coupled processes is needed, which is carried out satisfactorily. Then both
above-indicated flaws, related to the analysis of solely the
$\pi\pi$-scattering, are cured. The most remarkable change of parameters with
respect to the values of only $\pi\pi$ scattering analysis appears for the mass
of the $f_0 (600)$ which is now in some accordance with the Weinberg prediction
on the basis of mended symmetry and with an analysis using the large-$N_c$
consistency conditions between the unitarization and resonance saturation. The
obtained $\pi\pi$-scattering length $a_0^0$ in case when we restrict to the
analysis of the $\pi\pi$ scattering or consider so-called A-solution (with a
lower mass and width of $f_0(600)$ meson) agrees well with prediction of chiral
perturbation theory (ChPT) and with data extracted at CERN by the NA48/2
Collaboration from the analysis of the $K_{e4}$ decay and by the DIRAC
Collaboration from the measurement of the $\pi^+\pi^-$ lifetime.
