IMO 1989 LL POR84

Let a, b, c, r, and s be real numbers. Show that if r is a root of

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IMO 1989 LL POR84

Origin: POR

Problem

Let a, b, c, r, and s be real numbers. Show that if r is a root of ax2 +bx+c = 0 and s is a root of −ax2 +bx+c = 0, then a 2x2 +bx+c = 0 has a root between r and s.