1. Find the sum of the squares of the real roots of the equation $2 x^{4}-3 x^{3}+7 x^{2}-9 x+3=0$.
Answer: $\frac{5}{4}$
Solution: By synthetic division by $(x-1)$, we get
$$
\begin{aligned}
2 x^{4}-3 x^{3}+7 x^{2}-9 x+3 & =(x-1)\left(2 x^{3}-x^{2}+6 x-3\right) \\
& =(x-1)(2 x-1)\left(x^{2}+3\right) .
\end{aligned}
$$

Hence, the only real roots of $2 x^{4}-3 x^{3}+7 x^{2}-9 x+3=0$ are 1 and $\frac{1}{2}$. and the sum is $1+\frac{1}{4}=\frac{5}{4}$.