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When does the maximal root of this polynomial have unit magnitude? Prove an inverse linear relation between parameters
Examine the polynomial
$$
x^{\tau+1}-x^{\tau}+\alpha=0\,
$$
and denote by $\left|x_{\max}\left(\tau,\alpha\right)\right|$ as the
maximal magnitude of a root of this equation. For $\tau>1$, I ...