non-existence of positive real roots - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-24T02:34:29Z http://mathoverflow.net/feeds/question/107326 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/107326/non-existence-of-positive-real-roots non-existence of positive real roots Transcendental 2012-09-16T15:57:07Z 2012-09-16T15:57:07Z <p>Consider a cubic polynomial of the form [ \displaystyle f(x)=a_3x^3+a_2x^2+a_1x+a_0\;, ] where the coefficients are non-zero reals. Conditions for which this equation has three real simple roots are well-known. What conditions would guarantee that none of these roots is positive? In other words, what constraints on the parameters would guarantee that the polynomial has no positive roots? Please provide references also, if possible.</p>