Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 5 Polynomials and Polynomial Functions - 5.7 Apply the Fundamental Theorem of Algebra - Guided Practice for Example 4 - Page 382: 9

Answer

$1$ positive real zero, $2$ imaginary zeros

Work Step by Step

We are given the function: $$f(x)=x^3+2x-11.$$ First we count the number of sign changes: $$+,+,-.$$ The coefficients of $f(x)$ have one sign change, so $f$ has $1$ positive real zero. We determine $f(-x)$: $$f(-x)=(-x)^3+2(-x)-11=-x^3-2x-11.$$ We count the number of sign changes: $$-,-,-.$$ The coefficients of $f(-x)$ have no change of sign, therefore there is no negative real zero. To summarize, we got that the function has one positive real zero and two imaginary zeros.
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