lf $\alpha , \beta$ are the roots of $x^2+bx-c-0$, the the equation whose roots are $b$ and $c,$ is

Since$\alpha , \beta$ are roots of $x^2+bx-c=0$

$\therefore \alpha +\beta =-b,\alpha \beta =-c$

The equation whose roots are $b, c$ is

$\begin{array}{l}{x}^2-x(b+c)+bc=0\\ \Rightarrow x^2-x(-\alpha -\beta -\alpha \beta )+\alpha \beta (\alpha +\beta )=0\\ \Rightarrow x^2+x(\alpha +\beta +\alpha \beta )+\alpha \beta (\alpha +\beta )=0\end{array}$