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 294: 52

Answer

$2, -1+\sqrt 2 i, -1-\sqrt 2 i$

Work Step by Step

Consider $P(x)=x^3-x-6=0$ In order to get the zeroes of the polynomial $P(x)$ we will have to solve as follows: $x^3-x-6=(x-2)(x^2+2x+3)=0$ This gives: $(x-2)(\dfrac{1\pm\sqrt{1-4}}{2})=0$ This can be re-written as: $(x-2)(\dfrac{-2\pm\sqrt{4-12}}{2})=0$ $(x-2)(\dfrac{-2\pm i\sqrt {8}}{2})=0 $ Thus the zeroes of $P(x)$ are: $2, -1+\sqrt 2 i, -1-\sqrt 2 i$
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