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So I have this question in one of my exercises;

Determine explicitly the first three terms in the expansions of the three roots of $x^3− \epsilon (x^2)−\epsilon^2$.

Notice here the equation doesn't equate to zero. If it did I would go about doing this by setting

$$x = x(0) + \epsilon x(1) + \cdots$$

and then using the equating coefficients method for each of the epsilon ($\epsilon$) orders.

Do I have to set this equation equal to zero myself?

caverac
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user426307
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  • I am not sure if I understood correctly. If you are looking for roots of that cubic, however, then of course you must set the cubic equal to zero. – John Doe Apr 19 '18 at 12:24
  • I just tried doing this but when I do equate it to zero I am unable to find the three roots since x(0) = 0 – user426307 Apr 19 '18 at 15:03
  • Hmm, I think I understand the problem. Unfortunately I don't know the answer. Hopefully you get one soon! – John Doe Apr 19 '18 at 16:18

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