## non-existence of positive real roots [closed]

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.

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This can be answered using freshman calculus, so it's not appropriate for this site. – Deane Yang Sep 16 at 16:34
See the FAQ for suggestions of sites where this question might be appropriate. – Tom Leinster Sep 16 at 17:20