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Chapter 9: Q. 388 (page 977)

In the following exercises, solve each inequality algebraically and write any solution in interval notation.
-x2-4x-5<0

Short Answer

Expert verified

The solution in interval notation is (-鈭�,鈭�).

Step by step solution

01

Step 1. Given information.

The given inequality is:

-x2-4x-5<0

02

Step 2. Determine the critical points.

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

-x2-4x-5=0

Use the quadratic formula to solve the equation.

x=-(-4)卤(-4)2-4(-1)(-5)2(-1)鈭�x=-b卤b2-4ac2ax=4卤-4-2x=4卤2i-2x=-2卤i

03

Step 3. Determine the intervals where the inequality is true.

The complex solutions tell us the parabola does not intercept the x-axis.

Leading coefficient is -1. The negative leading coefficient represents that the parabola opens downwards.

Since for all values of x the graph is below the x-axis, all values of x makes the inequality true.

04

Step 4. Conclusion.

The solution in interval notation is (-鈭�,鈭�).

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