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## The Fundamental Theorem of Algebra

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**The Fundamental Theorem of Algebra**Lesson 4.5**Example**• Consider the solution to • Note the graph • No intersectionswith x-axis • Using the solve andcsolvefunctions**Fundamental Theorem of Algebra**• A polynomial f(x) of degree n ≥ 1 has at least one complex zero • Remember that complex includes reals • Number of Zeros theorem • A polynomial of degree n has at most n distinct zeros • Explain how theorems apply to these graphs**Constructing a Polynomial with Prescribed Zeros**• Given polynomial f(x) • Degree = 4 • Leading coefficient 2 • Zeros -3, 5, i, -i • Determine factored form • Determine expanded form**Conjugate Zeroes Theorem**• Given a polynomial with real coefficients • If a + biis a zero, then a – bi will also be a zero**Finding Imaginary Zeros**• Given • Determine all zeros • Use calculator to factor • Try cFactor command • Use calculator to graph • Use cSolve or cZeros**Application**• Complex numbers show up in study of electrical circuits • Impedance, Z • Voltage, V Can be represented by • Current, I complex numbers • Find missing value**Assignment**• Lesson 4.5 • Page 307 • Exercises 1 – 41 EOO 43 – 47 odd