I need to find the roots of the transcendental function,(adsbygoogle = window.adsbygoogle || []).push({});

f(x;a)=x^2-3ax-1-a+exp(-x/a)=0;

I've done many problems like this before and am fairly sure this is just a regular perturbation problem. The difficulty I'm having is with the exponential term.

Could anyone give me an idea of how to tackle this problem?

Thanks.

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# Perturbation theory and asymptotics

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