/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 70 Explain why the equation \(x^{4}... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 2: Problem 70

Explain why the equation \(x^{4}+6 x^{2}+2=0\) has no rational roots.

Short Answer

Expert verified
The equation \(x^{4}+6 x^{2}+2=0\) has no rational roots because, after applying the Rational Root Theorem and checking all possible rational roots, none of them satisfy the equation.

Step by step solution

01

Identify Polynomial Form and Coefficients

Identify the form of the polynomial. This equation is in the form of \(ax^{4} + bx^{2} + c = 0\). The coefficients are \(a = 1, b = 6, c = 2\).
02

Apply the Rational Root Theorem

According to the Rational Root Theorem, if the polynomial has a rational root \(p/q\), then \(p\) is a factor of the constant term (in this case 2) and \(q\) is a factor of the leading coefficient (in this case 1). Which means possible roots can be \(\pm1, \pm2\).
03

Substitute the Possible Roots

Substitute these possible roots into the equation and simplify to see if they satisfy the equation. Doing so for this problem, none of the possible roots satisfy the equation. Thus the given equation has no rational roots.

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

The perimeter of a rectangle is 50 feet. Describe the possible lengths of a side if the area of the rectangle is not to exceed 114 square feet.

Follow the seven steps on page 390 to graph rational function. $$f(x)=\frac{x^{2}-4 x+3}{(x+1)^{2}}$$

Use long division to rewrite the equation for \(g\) in the form $$\text {quotient }+\frac{\text {remainder}}{\text {divisor}}$$ Then use this form of the function's equation and transformations of \(f(x)=\frac{1}{x}\) to graph \(g.\) $$g(x)=\frac{2 x+7}{x+3}$$

a. Find the slant asymptote of the graph of each rational function and \(\mathbf{b} .\) Follow the seven-step strategy and use the slant asymptote to graph each rational function. $$f(x)=\frac{x^{2}+4}{x}$$

The equation for \(f\) is given by the simplified expression that results after performing the indicated operation. Write the equation for \(f\) and then graph the function. $$\frac{2}{x^{2}+3 x+2}-\frac{4}{x^{2}+4 x+3}$$
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

Probability and Statistics

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.