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if a diff.eqn. has the characteristic equation [itex]\lambda^2 + (3-K) \lambda + 1 = 0[/itex]

the eigenvalues solves to [itex]\lambda=-3/2 + K/2 \pm 1/2 \sqrt{5-6K+K^2}[/itex]. No problem there. But when is the diff.eqn. asymp. stable, meaning [itex]\Re(\lambda)<0[/itex] ?

I can only get this far

[itex]\Re(-3/2 + K/2 \pm 1/2*\sqrt{5-6K+K^2})<0[/itex]

[itex]-3/2+1/2 \Re(K \pm \sqrt{5-6K+K^2})<0[/itex]

How can i find the values for K, where this inequality is true?

Thanks

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# Re(eigenvalue) inequality problem

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