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how many roots does a polynomial with a degree of 6 have
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If the polynomial is nonzero and has degree 6, then by the Fundamental Theorem of Algebra it has exactly 6 complex roots counting multiplicity.
- Over the complex numbers: always 6 roots counted with multiplicity.
- Over the real numbers: it can have 6, 4, 2, or 0 real roots (counting multiplicity), since nonreal roots occur in conjugate pairs when coefficients are real.
- Special case: the zero polynomial (all coefficients zero) is not considered to have a degree and has infinitely many roots.
- Over the complex numbers: always 6 roots counted with multiplicity.
- Over the real numbers: it can have 6, 4, 2, or 0 real roots (counting multiplicity), since nonreal roots occur in conjugate pairs when coefficients are real.
- Special case: the zero polynomial (all coefficients zero) is not considered to have a degree and has infinitely many roots.
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