Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 3 - Review Exercises - Page 302: 74


$3$ zeros.

Work Step by Step

$(2t-1)^2-t^4=0\\4t^2-4t+1-t^4=0\\t^4-4t^2+4t-1=0\\(t^2+2t-1)(t^2-2t+1)=0\\(t^2+2t-1)(t-1)^2=0$. Thus $t^2+2t-1=0\\(t+1)^2-1-1=0\\(t+1)^2=2\\t+1=\pm\sqrt2\\t=-1\pm\sqrt2$ or $(t-1)^2=0\\t-1=0\\t=1$ Thus the polynomial has $3$ zeros.
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