Solution
= Solution
Exactness for $1$ and $x$ gives
$$
a_0+a_1=\frac12,\qquad a_0x_0+a_1x_1=\frac13.
$$
Hence
$$
\boxed{a_0=\frac{x_1/2-1/3}{x_1-x_0},\qquad
a_1=\frac{1/3-x_0/2}{x_1-x_0}.}
$$
= Solution
Exactness for $1$ and $x$ gives
$$
a_0+a_1=\frac12,\qquad a_0x_0+a_1x_1=\frac13.
$$
Hence
$$
\boxed{a_0=\frac{x_1/2-1/3}{x_1-x_0},\qquad
a_1=\frac{1/3-x_0/2}{x_1-x_0}.}
$$