Four Roots on a Circle

★ 7/10complex numbers Quadratic Equations Circles Casework

Problem

The real-coefficient equations

x^2 - 2x + 2 = 0 \qquad\text{and}\qquad x^2 + 2mx + 1 = 0

have four distinct roots whose points in the complex plane are concyclic. Find the range of $m$ .

Answer

Solution

Difficulty	7/10
Topics	complex numbers, Quadratic Equations, Circles, Casework

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