The Fundamental Theorem of Algebra Section 4.6 beginning on page 198.

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Presentation transcript:

The Fundamental Theorem of Algebra Section 4.6 beginning on page 198

The Fundamental Theorem of Algebra

Finding the Zeros of a Polynomial (We will test together on the board) ** Once you find one, divide into the NEW quotient. Once you get down to a quadratic you can factor the rest if possible)

The Complex Conjugates Theorem

Using Zeros to Write a Polynomial

Descartes’s Rule of Signs

Using Descartes’s Rule of Signs 3 sign changes  3 or 1 positive real zeros. 3 sign changes  3 or 1 negative real zeros. Positive RealNegative RealImaginaryTotal We know that there are 6 solutions (the degree of the polynomial is 6)

Monitoring Progress

1) 2) Positive RealNegative RealImaginaryTotal 1023 Positive RealNegative RealImaginaryTotal