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: 61

Answer

$x=7.8\ in$ and $x=10\ in$
1582136727

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 $V=2000$, we have $x^3-5x^2-150x+1000=0$ Step 2. Using synthetic division, we can find a zero at $x=10$, as shown in the figure, and the above equation becomes $(x-10)(x^2+5x-100)=0$ Step 3. As $x\geq0$, the second solution can be found as $x=\frac{-5+5\sqrt {17}}{2}\approx7.8\ in$ Step 4. We conclude the two possible solutions are $x=7.8\ in$ and $x=10\ in$
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