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Choose three numbers $\lambda_1,\lambda_2,\lambda_3$. Compute the coefficients $a,b,c$ of the polynomial $(x-\lambda_1)(x-\lambda_2)(x-\lambda_3) = x^3-ax^2-bx-c$. Choose $s_i$ and $f_i$ such that $f_0=a$, $f_1s_0=b$, $f_2s_0s_1=c$. It shouldn't be hard to play around with the coefficients so that those inequalities are satisfied, since you have so many ...


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