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Notes 6.6 Fundamental Theorem of Algebra

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If P(x) is a polynomial with degree n >1 with complex coefficients, then P(x) = 0 has at least one complex root.

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An nth degree polynomial equation has exactly n roots; related polynomial function has exactly n zeros. If you factor a polynomial of degree n, then it has n linear factors.

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EX 1 x 4 – 3x 3 + 4x + 1 = 0 State the number of complex roots, the possible number of real roots, and the possible rational roots.

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EX 2 State the number of complex roots, the possible number of real roots, and the possible rational roots. x 3 + 2x 2 – 4x – 6 = 0

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EX 3 Find all the zeros. x 5 + 3x 4 – x - 3

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