= Quarter-sector winding test for a real quartic
Suppose a monic real <quartic polynomial> has no nonnegative real zero and its real part on the imaginary axis is everywhere positive. For sufficiently large $R$, its image of the quarter-circle arc from $R$ to $iR$, closed by the straight chord from $p(iR)$ to $p(R)$, has <winding number> one: compare with $z^4$ on the arc and its constant image on the chord. The rest of the actual sector boundary maps into the right half-plane, so its replacement by that chord preserves the winding number. The <argument principle> then counts exactly one root in the open first quadrant, including multiplicity.
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