24th ASU 1990 Problem 6 Find three non-zero reals such that all quadratics with those numbers as coefficients have two distinct rational roots.
1,2,-3 Solution If a + b + c = 0, then 1 is a root of ax 2 + bx + c, and so the other root is -b/a - 1, which is rational. 24th ASU 1990 © John Scholes jscholes@kalva.demon.co.uk 2 March 2004 Last corrected/updated 2 Mar 04