Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 2 - Section 2.5 - Zeros of Polynomial Functions - Exercise Set - Page 378: 62


$x=5\ in$ and $x=12.2\ in$

Work Step by Step

Step 1. Use the given formula $V=x(x+10)(30-2x)=x(30x-2x^2+300-20x)=-2x^3+10x^2+300x$ and letting $V=1500$, we have $x^3-5x^2-150x+750=0$ Step 2. Using synthetic division, we can find a zero at $x=5$, as shown in the figure, and the above equation becomes $(x-5)(x^2-150)=0$ Step 3. As $x\geq0$, the second solution can be found as $x=\sqrt {150}\approx12.2\ in$ Step 4. We conclude the two possible solutions are $x=5\ in$ and $x=12.2\ in$
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