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Chapter 9: Q. 385 (page 977)

In the following exercises, solve each inequality algebraically and write any solution in interval notation.

x2+3x+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+3x+5>0

02

Step 2. Determine the critical points.

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

x2+3x+5=0

Use the quadratic formula to solve the equation.

x=-(3)卤(3)2-4(1)(5)2(1)鈭�x=-b卤b2-4ac2ax=-3卤-112x=-3卤11i2

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 positive leading coefficient represents that the parabola opens upwards.

Since for all values of x the graph is above 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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