Solution
= Solution
Symmetry gives nodes $\pm c$ with equal weights $b$. Exactness for $1$ and $x^2$ requires
$$
2b=\int_{-1}^1x^2dx=\frac23,
\qquad
2bc^2=\int_{-1}^1x^4dx=\frac25.
$$
Therefore
$$
\boxed{b_1=b_2=\frac13,
\qquad c_1=-\sqrt{\frac35},
\quad c_2=\sqrt{\frac35}}.
$$
Odd moments vanish automatically, so the rule is exact through degree three.