Solution
= Solution
Because $a_0\ne0$, the lowest-power equation from part (b) requires the <indicial equation>
$$
4\sigma^2-8\sigma+3=(2\sigma-1)(2\sigma-3)=0.
$$
The two candidate <indicial roots> are therefore
$$
\boxed{\sigma=\frac12\quad\text{and}\quad\sigma=\frac32.}
$$
Their difference is the integer one, so the smaller-root coefficient equation at $k=1$ needs examination rather than automatic division.