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Complex Conjugate Roots of a Cubic - Cardon's Method

Can you show me how to work this? Is there only one way and what is most acceptable?
Find the values of the complex conjugate roots for the equation x^3 + 3X^2 +2 = 0.

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To find the roots of a cubic equation, we generally use Cardon's method (although it is a bit tedious, it is the most acceptable algebraic method of solving a cubic).
The solution file is attached.