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: 20

Answer

Solution set: $ (-2,0)$
1510349558

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. $x^{2}+2x < 0$ $f(x)=x^{2}+2x \quad $...factor the trinomial... $f(x)=x(x+2)$ $x(x+2) < 0$ 2. Solve the equation $f(x)=0$. The real solutions are the boundary points. $x(x+2) =0$ $x=-2$ or $x=0$ 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, $\begin{array}{llll} Intervals: & (-\infty, -2) & (-2,0) & (0,\infty)\\ a=test.val. & -3 & -1 & 1\\ f(a) & (-3)(-1) & (-1)(-1) & (1)(3)\\ f(a) < 0 ? & F & T & F \end{array}$ 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: $ (-2,0)$
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