Know the Fundamental Theorem of Algebra and connect it to polynomial roots.
Find missing polynomial roots from the degree, counting multiplicity
Problem
A real-coefficient cubic has roots \(2\) and \(1~+~i\). Find the remaining root.
Big Picture
What this problem is really about
A polynomial with real coefficients cannot have an unpaired nonreal root. Complex conjugation keeps the real part and reverses only the imaginary sign, producing the companion root required by the conjugate-root theorem. After supplying that partner, count all known roots with multiplicity to confirm that they fill the polynomial's degree.
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