\section*{Problem 6}

Find three non-zero reals such that all quadratics with those numbers as coefficients have two distinct rational roots.

Answer \(1,2,-3\)


\section*{Solution}

If \(\mathrm{a}+\mathrm{b}+\mathrm{c}=0\), then 1 is a root of \(\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}\), and so the other root is \(-\mathrm{b} / \mathrm{a}-1\), which is rational.

