Notes 6.6 Fundamental Theorem of Algebra. If P(x) is a polynomial with degree n >1 with complex...

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Notes 6.6 Fundamental Theorem of Algebra

Transcript of Notes 6.6 Fundamental Theorem of Algebra. If P(x) is a polynomial with degree n >1 with complex...

Page 1: Notes 6.6 Fundamental Theorem of Algebra. If P(x) is a polynomial with degree n >1 with complex coefficients, then P(x) = 0 has at least one complex root.

Notes 6.6 Fundamental Theorem of Algebra

Page 2: Notes 6.6 Fundamental Theorem of Algebra. If P(x) is a polynomial with degree n >1 with complex coefficients, then P(x) = 0 has at least one complex root.

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

Page 3: Notes 6.6 Fundamental Theorem of Algebra. If P(x) is a polynomial with degree n >1 with complex coefficients, then P(x) = 0 has at least one complex root.

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.

Page 4: Notes 6.6 Fundamental Theorem of Algebra. If P(x) is a polynomial with degree n >1 with complex coefficients, then P(x) = 0 has at least one complex root.

EX 1

x4 – 3x3 + 4x + 1 = 0 State the number of complex roots, the

possible number of real roots, and the possible rational roots.

Page 5: Notes 6.6 Fundamental Theorem of Algebra. If P(x) is a polynomial with degree n >1 with complex coefficients, then P(x) = 0 has at least one complex root.

EX 2

State the number of complex roots, the possible number of real roots, and the possible rational roots.

x3 + 2x2 – 4x – 6 = 0

Page 6: Notes 6.6 Fundamental Theorem of Algebra. If P(x) is a polynomial with degree n >1 with complex coefficients, then P(x) = 0 has at least one complex root.

EX 3

Find all the zeros. x5 + 3x4 – x - 3


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Every polynomial P(x) of degree n>0 has at least one zero in the complex number system.

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