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Chapter 4: Q. 24 (page 241)

Solve the inequality algebraically

3x3<-15x2

Short Answer

Expert verified

Required solution set is (-∞,-5).

Step by step solution

01

Step 1. Given information  

We are given an inequality,

3x3<-15x2

02

Step 2.Finding the zeros   

The zeros is given by,

3x3=-15x23x3+15x2=03x2(x+5)=03x2=0x=0x+5=0x=-5

So, the intervals will be,

(-∞,-5),(-5,0),and(0,∞)

03

Step 4. Selecting a test number in each interval  

The table is as follows,

Interval(-∞,-5)
(-5,0)
(0,∞)
Chosen Number -6
 -1
 1
Value of Functionf(-6)=-108f(-1)=12f(1)=18
CheckNegativePositive
Positive

Hence the solution set is (-∞,-5).

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Most popular questions from this chapter

United Parcel Service has contracted you to design a closed box with a square base that has a volume of 10,000cubic inches. See the illustration.

Part (a): Express the surface area S of the box as a function of x.

Part (b): Using a graphing utility, graph the function found in part (a).

Part (c): What is the minimum amount of cardboard that can be used to construct the box?

Part (d): What are the dimensions of the box that minimize the surface are?

Part (e): Why might UPS be interested in designing a box that minimizes the surface area?

Find the real zeros of f. Use the real zeros to factor f. f(x)=x4+x3-3x2-x+2

In Problems 21–32, determine the maximum number of real zeros that each polynomial function may have. Then list the potential rational zeros of each polynomial function. Do not attempt to find the zeros.

f(x)=x5-x4+2x2+3

Find the domain of the rational function.

Rx=4xx-3

Solve the inequality algebraically

(x-1)(x-2)(x-3)≤0
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