Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 3 - Review - Exercises - Page 321: 42

Answer

(a) $\pm1,\pm1/2\pm1/3,\pm1/6,\pm2,\pm2/3,\pm4,\pm4/3$ (b) 0 positive, 4, 2 or 0 negative real zeros.

Work Step by Step

(a) $p=\pm1,\pm2,\pm4,q=\pm1,\pm2,\pm3,\pm6$ $\frac{p}{q}=\pm1,\pm1/2\pm1/3,\pm1/6,\pm2,\pm2/3,\pm4,\pm4/3$ (b) $P(x)$ has zero sign changes, so there are 0 positive real zeros. $P(-x)=6x^4-3x^3+x^2-3x+4$ and there are 4 sign changes, so there may be 4, 2 or 0 negative real zeros.
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