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.
closed as off topic by Michael Renardy, Deane Yang, S. Sra, Andres Caicedo, Tom Leinster Sep 16 at 17:19