Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 3: Q. 41 (page 172)

Explain why the inequality x2+x+1>0has all real numbers as the solution set.

Short Answer

Expert verified
  • The entire curve lies above the x-axis.
  • So, all the values in the domain of the function are the solution of the given inequality.

Step by step solution

01

Step 1. Given Information

The given inequality isx2+x+1>0.

02

Step 2. Find the Intercepts

  • Consider the function f(x)=x2+x+1.
  • The function cannot be factored further.
  • There are no x-intercepts of the curve.
  • The value off(0) is 1.
  • So, the y-intercept is 1.
  • This implies that the entire curve lies above the x-axis.
  • So, all the values in the domain of the function are the solution of the given inequality.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In Problems 25–32, use the given functions f and g.

(a)f(x)=0(b)g(x)=0(c)f(x)=g(x)(d)f(x)>0

(e)g(x)≤0(f)f(x)>g(x)(g)f(x)≥1

f(x)=-x2+3g(x)=-3x+3

In Problems 7–22, solve each inequality.

4x2+9<6x

In Problems 7–22, solve each inequality.

25x2+16<40x

Graph the function fby starting with the graph of y=x2and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

Hint: If necessary, write fin the form f(x)=a(x-h)2+k.

f(x)=3x2+6x

Graph the function fby starting with the graph of y=x2and using transformations (shifting, compressing, stretching, and/or reflection). Verify your results using a graphing utility.

f(x)=14x2
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Discrete Mathematics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free