College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 3 - Polynomial and Rational Functions - Exercise Set 3.6 - Page 420: 29

Answer

Solution set: $[1,2]\cup[3,\infty)$
1510354141

Work Step by Step

Follow the "Procedure for Solving Polynomial lnequalities",\ p.412: 1. Express the inequality in the form $f(x)<0, f(x)>0, f(x)\leq 0$, or $f(x)\geq 0,$ where $f$ is a polynomial function. $(x-1)(x-2)(x-3)\geq 0$ $f(x)=(x-1)(x-2)(x-3)$ 2. Solve the equation $f(x)=0$. The real solutions are the boundary points. $(x-1)(x-2)(x-3)=0$ $x=1$ or $x=2$ or $x=3$ 3. Locate these boundary points on a number line, thereby dividing the number line into intervals. 4. Test each interval's sign of $f(x)$ with a test value, $\begin{array}{llll} Intervals: & a=test.v. & f(a),signs & f(a) \geq 0 ? \\ (-\infty,1) & 0 & (-)(-)(-) & F\\ (1,2) & 1.5 & (+)(-)(-) & T\\ (2,3) & 2.5 & (+)(+)(-) & F\\ (3,\infty) & 5 & (+)(+)(+) & T \end{array}$ 5. Write the solution set, selecting the interval or intervals that satisfy the given inequality. If the inequality involves $\leq$ or $\geq$, include the boundary points. Solution set: $[1,2]\cup[3,\infty)$
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