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Jun 28, 2017 at 12:28 comment added Dima Pasechnik @DenisSerre I am aware of hyperbolic polynomials, but they appear to be sort of orthogonal concept---they have all roots real, as opposed to (generically) having no real roots.
Jun 28, 2017 at 11:19 comment added Denis Serre Perhaps you should learn about hyperbolic polynomials, a notion due to Garding.
Jun 22, 2017 at 8:41 vote accept Dima Pasechnik
Jun 21, 2017 at 11:25 comment added Dima Pasechnik I've edited the question to work this comment in.
Jun 21, 2017 at 11:16 history edited Dima Pasechnik CC BY-SA 3.0
worked in the Ivan's comment.
Jun 21, 2017 at 11:07 comment added Dima Pasechnik thanks, right---as I need something that "works" in $\mathbb{R}[a,b,c]$ I missed that indeed my conditions are equivalent to the eigenvalues of the 2x2 matrix in question being positive semidefinite...
Jun 21, 2017 at 10:31 answer added darij grinberg timeline score: 3
Jun 21, 2017 at 10:28 comment added Ivan Izmestiev One classical generalization is the convexity of the cone of positive semidefinite quadratic forms.
S Jun 21, 2017 at 10:10 history edited Dima Pasechnik CC BY-SA 3.0
Minor edits
S Jun 21, 2017 at 10:10 history suggested Rodrigo de Azevedo CC BY-SA 3.0
Minor edits
Jun 21, 2017 at 10:06 review Suggested edits
S Jun 21, 2017 at 10:10
Jun 21, 2017 at 9:12 history asked Dima Pasechnik CC BY-SA 3.0