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Fundamental Theorem of Algebra

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Presentation on theme: "Fundamental Theorem of Algebra"— Presentation transcript:

1 Fundamental Theorem of Algebra
Section 5.3 Complex Zeros; Fundamental Theorem of Algebra Copyright © 2013 Pearson Education, Inc. All rights reserved

2 Copyright © 2013 Pearson Education, Inc. All rights reserved

3 Copyright © 2013 Pearson Education, Inc. All rights reserved

4 Copyright © 2013 Pearson Education, Inc. All rights reserved

5 Copyright © 2013 Pearson Education, Inc. All rights reserved

6 A polynomial of degree 5 whose coefficients are real numbers has the zeros –2, –3i, and 2 + 4i. Find the remaining two zeros. Since f has coefficients that are real numbers, complex zeros appear as conjugate pairs. It follows that 3i, the conjugate of –3i, and 2 – 4i, the conjugate of 2 + 4i, are the two remaining zeros. Copyright © 2013 Pearson Education, Inc. All rights reserved

7 Try This: p. 363 # 11 Copyright © 2013 Pearson Education, Inc. All rights reserved

8 Copyright © 2013 Pearson Education, Inc. All rights reserved

9 Find a polynomial f of degree 4 whose coefficients are real numbers and that has the zeros 1, 1, 4+i. Since 4 + i is a zero, by the Conjugate Pairs Theorem, 4 – i is also a zero. By the factor theorem: Copyright © 2013 Pearson Education, Inc. All rights reserved

10 Try This: p. 363 # 19 Copyright © 2013 Pearson Education, Inc. All rights reserved

11 Copyright © 2013 Pearson Education, Inc. All rights reserved

12 Step 1: The degree of f is 4 so there will be 4 complex zeros.
Copyright © 2013 Pearson Education, Inc. All rights reserved

13 Copyright © 2013 Pearson Education, Inc. All rights reserved

14 Try This p. 364 # 35 Copyright © 2013 Pearson Education, Inc. All rights reserved

15 Homework P. 363 Pencil problems and 14, 20, 34, 38
Copyright © 2013 Pearson Education, Inc. All rights reserved

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