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Omni-MATH / Let n be a positive integer, n≥2, and consider the polynomial equation

Problem

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problem

Let nn be a positive integer, n≥2n \geq 2, and consider the polynomial equation xn−xn−2−x+2=0.x^n - x^{n-2} - x + 2 = 0. For each n,n, determine all complex numbers xx that satisfy the equation and have modulus |x|=1.|x| = 1.
Plain-text mathematical notation (without MathML)
Let n be a positive integer, n≥2, and consider the polynomial equation
x^(n)−x^(n−2)−x+2=0.
For each n, determine all complex numbers x that satisfy the equation and have modulus |x|=1.
Original LaTeX notation
Let $n$ be a positive integer, $n \geq 2$, and consider the polynomial equation
\[x^n - x^{n-2} - x + 2 = 0.\]
For each $n,$ determine all complex numbers $x$ that satisfy the equation and have modulus $|x| = 1.$

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Source and history

task_id
0769814e-65c3-57de-a049-de307b6b5f53
task_key
test--0769814e-65c3-57de-a049-de307b6b5f53
task_revision_id
1
config / split
/ test

Official source

initial import