Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 3 - Section 3.5 - Complex Zeros and the Fundamental Theorem of Algebra - 3.5 Exercises - Page 293: 18

Answer

(a) $-1,2,\frac{1\pm\sqrt 3i}{2},-1\pm\sqrt 3i$ (b) $P(x)=(x-2)(x+1)(x+1+\sqrt 3i)(x+1-\sqrt 3i)(x-\frac{1+\sqrt 3i}{2})(x-\frac{1-\sqrt 3i}{2})$

Work Step by Step

(a) $P(x)=(x^3-8)(x^3+1)=(x-2)(x^2+2x+4)(x+1)(x^2-x+1)$ The zeros are $-1,2,\frac{1\pm\sqrt 3i}{2},-1\pm\sqrt 3i$ (b) $P(x)=(x-2)(x+1)(x+1+\sqrt 3i)(x+1-\sqrt 3i)(x-\frac{1+\sqrt 3i}{2})(x-\frac{1-\sqrt 3i}{2})$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.