Let these roots are $\frac{a}{d},\frac{b}{d}, \frac{c}{d}$ where $d$ is positive integer and $a,b,c$ are integers $\frac{a+b+c}{d}=2023, \frac{ab+bc+ca}{d^2}=-2023$ and so $\frac{a^2+b^2+c^2}{d^2}=2023^2+2*2023=2023*2025$ or $a^2+b^2+c^2+d^2=2024^2d^2$ But $n^2 \equiv 0,1,4 \pmod {8}$ and so $8|a^2+b^2+c^2+d^2 \to 2|a,b,c,d$ and so with infinine descent we can prove, that only solution is $a=b=c=d=0$ which is impossible.