Perturbation Expansion

50 Views Asked by At

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?