Precalculus: Mathematics for Calculus, 7th Edition

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

Chapter 3 - Section 3.7 - Polynomial and Rational Inequalities - 3.7 Exercises - Page 316: 13

Answer

$[-5, 1] U [3, ∞)$

Work Step by Step

$x^3 + x^2 - 17x + 15 \geq 0$ Find the roots of the function $x^3 + x^2 - 2x - 15x + 15$ $x (x^2 + x - 2) - 15(x-1)$ $x (x+2)(x-1) - 15(x-1)$ $(x-1)(x^2 + 2x -15)$ $(x+5)(x-1)(x-3)$ $x = -5, 1, 3$ Test numbers in between those zero values to determine if the function is negative or positive (-∞, -5] $(-)(-)(-) = (-)$ [-5, 1] $(+)(-)(-) = (+)$ [1, 3] $(+)(+)(-) = (-)$ [3, ∞) $(+)(+)(+) = (+)$ Thus the solution is $[-5, 1] U [3, ∞)$
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