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Chapter 9: Q 9.132 (page 973)

Solve the following quadratic inequality algebraically and write the solution in interval notation.

x2-2x-15鈮�0

Short Answer

Expert verified

The solution, in interval notation, is -3,5.

Step by step solution

01

Step 1. Given Information

The inequality in standard form is x2-2x-15鈮�0.

Change the inequality sign to an equal sign and then solve the equation.

x2-2x-15=0x2-5x+3x-15=0x-5x+3=0x=5,x=-3

02

Step 2. Test point

Use the critical points -3and 5 to divide the number line into intervals.

The above number line shows the sign of each quadratic expression using test points from each interval.

Take test pointsx=-5,x=0,x=6

03

Step 3. Check sign of inequality

Check the inequality sign for the above test points.

For x=-5,

x2-2x-15=(-5)2-2(-5)-15=25+10-15=20

For x=0,

x2-2x-15=(0)2-2(0)-15=-15

For x=6,

x2-2x-15=(6)2-2(6)-15=36-12-15=9

04

Step 4. Solution of the inequality in interval notation

The inequality is negative in the second interval only.

The expression equals 0 at points -3and 5.

The solution, in interval notation, is -3,5.

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