# How does one solve a cubic polynomial with complex coefficients?

I have found formulas online for the the roots of a cubic polynomial with real coefficients, but they all said this they would not work for polynomials with complex coefficients. I need to solve the following: $x^3+cx^2+\alpha$ where $c>0$ and $\alpha\in\mathbb{C}$. Anyone have the formula

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In my answer here, I give a cubic formula that works for complex coefficients and works with the way principal roots are defined on non-real complex numbers in the vast majority of calculators and computer algebra systems.

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