## a problem about All roots in the left half plane

Suppose a polynomial$u(x)=ax^{2}+bx+c$，with a b c positive,$g(x)=d*xe^{-\lambda_1 x}+fe^{-\lambda_2 x}$with d,f positve, let $H(x)=u(x)-g(x)$, when we reserach some bahavior of a dynamic system, we want to give some condtion such that all root of H(x) will locate in the half-left complex, however I did not how to deal with, any reference and advice will be appreatiated.

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 Why is this tagged fourier- and real-analysis? Wouldn't it be better to tag it complex analysis and/or dynamical systems given the question stated? Also, is the asterisk sign $*$ the usual product of complex numbers, or something else? – Willie Wong Mar 26 2012 at 10:37 @Willie Wong， I am sorry，It is just means times – yaoxiao Mar 26 2012 at 13:33