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Published byValerie Bailey Modified over 6 years ago

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Lesson 2.5 The Fundamental Theorem of Algebra

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For f(x) where n > 0, there is at least one zero in the complex number system Complex → real and imaginary Real zeros → can see on graph Imaginary → cannot see on graph Complex zeros always occur in conjugate pairs “If a + bi is a zero, then a – bi is also” f(x) of degree n will have exactly n zeros (real and imaginary)

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How do we find the zeros of For a polynomial f(x) with degree n: 1)Find real zero(s) using calculator or Factor Theorem and Synthetic Division If there are n real roots, stop 2)Divide out real zeros to obtain a 2 nd degree equation 3)Solve 2 nd degree equation for x (use Quadratic Equation if necessary)

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Example 1

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Example 2 Problem Set 2.5

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