Solving (1/2)x^4-x^2-1=0: A Comprehensive Guide

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Homework Help Overview

The discussion revolves around solving the polynomial equation (1/2)x^4 - x^2 - 1 = 0, which falls under the subject area of algebra, specifically polynomial equations.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants suggest various approaches, including substituting t = x^2 and multiplying the equation by 2 to eliminate fractions. There is also mention of using "guess and check" to find roots and then applying polynomial long division.

Discussion Status

The discussion is active, with participants encouraging the original poster to share their attempts. Several strategies have been proposed, but there is no explicit consensus on a single method to solve the equation.

Contextual Notes

Some participants express the need for the original poster to provide more of their work to facilitate better assistance, indicating a preference for collaborative problem-solving.

nameVoid
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(1/2)x^4-x^2-1=0
 
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try let t=x^2
by the way, you'd better show at least some of your attempt first, people do not like to answer a question shown in this way
 
Yes, let's see some work nameVoid!

Another hint, if you don't like fractions, is to multiple both sides of the equation by 2.


01
 
A popular strategy to get the first root to this type of problem is "guess and check". After you've guessed one root, which is easy to do in this case, you can do polynomial long division to reduce the order of the polynomial and get an equation you may be more familar with solving.
 

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