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