evaluate number of poles lying on the right,left side of s-plane and on the jw-axis?
Maybe your MatLab script is wrong. I try with Octave

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&gt;&gt;roots([0.5 3 2 3 2 1])

ans =

  -5.44527 + 0.00000i
   0.17829 + 0.92802i
   0.17829 - 0.92802i
  -0.45565 + 0.45131i
  -0.45565 - 0.45131i

&gt;&gt;


and it shows two right-half plane roots.

Your MatLab output shows two right-half plane roots, but different values.

Revision

With a new lecture of your question, I note that the coefficient of \$s^ 5\$ is not 0.5. The transfer function is

\$
T(s)=\dfrac{1}{2s^5+3s^4+2s^3+3s^2+2s+1}
\$

and using Octave to find the roots of denominator

&gt;&gt; roots([2 3 2 3 2 1])
ans =

  -1.33069 + 0.00000i
   0.32844 + 0.88991i
   0.32844 - 0.88991i
  -0.41309 + 0.49692i
  -0.41309 - 0.49692i

&gt;&gt;


that is the same result as your MatLab execution.

The transfer function has 5 poles, 1 real and 4 complex. Two complex poles has positive real part, that is, two poles are on the right-half plane.