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- The third and thus last solution of $x^3 + \alpha x + \beta = 0$ is
- \[x = \frac{(1-i \sqrt{3}) \alpha}{\sqrt[3]{12} \cdot t}
- -\frac{(1+i\sqrt{3}) t}{2\sqrt[3]{18}}\]
- The complex conjugate root theorem states
- that if $x$ is a complex root of a polynomial $P$, then its
- complex conjugate $\overline{x}$ is also a root of $P$.
- The solution presented in this case is the complex conjugate of
- case 2.2.
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