Prime Quartic With k-Narrative

Algebra Level pending

Let f ( x ) = a x 4 + ( a e + k ) x 3 + k e x 2 + x + e f(x)=ax^4+(ae+k)x^3+kex^2+x+e where prime a > 2 a>2 , prime ∣ e ∣ > 1 |e|>1 . Find integer k k such that f ( x ) f(x) has exactly two rational roots.

k = 1 − a 2 k=1-a^2 k = 1 + a 2 k=1+a^2 k = 1 − e 2 k=1-e^2 k = 1 + e 2 k=1+e^2

Frank Giordano by Frank Giordano , 57, USA

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1 solution

Frank Giordano
Sep 27, 2016

this facebook video explains the Game of G-filtered Polycules for Cubics; leave a comment.

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get the latest version of "G-filtered Polycules" here: https://www.facebook.com/groups/factorthis/

Frank Giordano - 4 years, 7 months ago

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