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Chapter 3: Q. 18 (page 174)

In Problems 18鈥�19, solve each quadratic inequality.

x2+6x-16<0

Short Answer

Expert verified

The solution of inequality is x|-8<x<2or interval notation-8,2.

Step by step solution

01

Step 1. Given information.

Solve the given quadratic inequality.

x2+6x-16<0

02

Step 2. Graph the function.

Graph the function f(x)=x2+6x-16.

03

Step 3. Find intercept.

y- intercept: f(0)=02+60-16=-16

x-intercept : Solve f(x)=0

x2+6x-16=0x1,2=-b卤b2-4ac2ax1,2=-6卤62-4路1路-162路1x1,2=-6卤36+642x1,2=-6卤1002x1,2=-6卤102x1=-6+102,x2=-6-102x1=2,x2=-8

So, the x-intercept are x1=2andx2=-8

The graph is below the x-axis f(x)<0between the x=-8andx=2. Since the inequality is strict the solution set isx-8<x<2or using interval notation-8,2.

04

Step 4. Conclusion.

The solution set of inequality isx-8<x<2or interval notation-8,2.

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