Problem

Source: Iranian National Olympiad (3rd Round) 2007

Tags: algebra, polynomial, geometry, rhombus, algebra proposed



Let $ a,b$ be two complex numbers. Prove that roots of $ z^{4}+az^{2}+b$ form a rhombus with origin as center, if and only if $ \frac{a^{2}}{b}$ is a non-positive real number.