Finding Roots in the Equation x^4+x^3-4x^2-1=0

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Homework Help Overview

The discussion revolves around the equation x^4+x^3-4x^2-1=0, with participants exploring methods to find its roots. The subject area includes polynomial equations and potentially numerical methods for root finding.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants express uncertainty about how to begin solving the equation, particularly due to the presence of the constant term -1. Some suggest using the rational root test, while others mention the possibility of numerical approximations or refer to external resources for solving quartic equations.

Discussion Status

The discussion is ongoing, with participants questioning the clarity of the original problem statement and exploring various approaches to tackle the equation. There is no explicit consensus on a method yet, but guidance has been offered regarding potential strategies.

Contextual Notes

Some participants note the lack of "nice" roots for the equation, indicating that traditional factoring methods may not be effective. There is also a request for clarification on the exact wording of the problem statement, suggesting potential ambiguity in the homework assignment.

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Homework Statement



show that the equation x^4+x^3-4x^2-1=0

Homework Equations





The Attempt at a Solution


I wasn't sure where to start. The minus one at the end really threw me off. I tried to factor by grouping by coul;dn't figure out what to do with the -1
 
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Have you learned the rational root test?
 
ryan.1015 said:

Homework Statement



show that the equation x^4+x^3-4x^2-1=0

Homework Equations





The Attempt at a Solution


I wasn't sure where to start. The minus one at the end really threw me off. I tried to factor by grouping by coul;dn't figure out what to do with the -1

What's the rest of the sentence?
show that the equation x^4+x^3-4x^2-1=0

Show that this equation does what?

Please give us the exact wording of the problem.
 

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