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

  • Thread starter Thread starter nameVoid
  • Start date Start date
Click For Summary
SUMMARY

The discussion focuses on solving the polynomial equation (1/2)x^4 - x^2 - 1 = 0. A recommended approach is to substitute t = x^2, simplifying the equation. Participants emphasize the importance of demonstrating initial attempts to facilitate assistance. Additionally, multiplying both sides by 2 is suggested to eliminate fractions, and using the "guess and check" method followed by polynomial long division is highlighted as an effective strategy for finding roots.

PREREQUISITES
  • Understanding polynomial equations and their roots
  • Familiarity with substitution methods in algebra
  • Knowledge of polynomial long division
  • Basic skills in manipulating fractions and equations
NEXT STEPS
  • Research polynomial root-finding techniques
  • Learn about the substitution method in algebra
  • Study polynomial long division in detail
  • Explore the "guess and check" method for solving equations
USEFUL FOR

Students, educators, and anyone interested in mastering polynomial equations and algebraic problem-solving techniques.

nameVoid
Messages
238
Reaction score
0
(1/2)x^4-x^2-1=0
 
Physics news on Phys.org
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.
 

Similar threads

Solve ##x^{\frac{-1}{2}}-2x^{\frac{1}{2}}+x^{\frac{2}{3}}=0##
  • · Replies 24 ·
Replies
24
Views
3K
How Do You Solve the Inequality ##x^2<4## for Negative Values of ##x##?
  • · Replies 6 ·
Replies
6
Views
3K
Solve the given simultaneous equations in x^2, x and y
  • · Replies 1 ·
Replies
1
Views
1K
Show that if ##x>1##, ##\log_e\sqrt{x^2-1}=\log_ex-\dfrac{1}{2x^2}-##
  • · Replies 8 ·
Replies
8
Views
2K
If ##x> 1## and ##x^2 <2##, prove ##x < y##, ##y^2<2##
  • · Replies 10 ·
Replies
10
Views
2K
Solve ##\sqrt{\dfrac{x}{y}}+\sqrt{\dfrac{y}{x}}=4\dfrac{1}{4} \cdots##
  • · Replies 10 ·
Replies
10
Views
2K
Master Factorization with Step-by-Step Guide for x^4 - 3x^2 - 4
  • · Replies 19 ·
Replies
19
Views
3K
Show that ##f(x)=2',1',2'## in the irreducible Polynomial
  • · Replies 8 ·
Replies
8
Views
2K
Find the range of the function ##f(x) = \frac{e^{2x}-e^x+1} {e^{2x}+e^x+1}##
  • · Replies 8 ·
Replies
8
Views
4K
##f(x+y) =f(x) f(y)## and ##f(1)+f(2)=5## then find ##f(-1)=?##
  • · Replies 49 ·
2
Replies
49
Views
4K