Cubic non-linear inequality (HELP)

Click For Summary

Discussion Overview

The discussion revolves around a cubic non-linear inequality that a participant is struggling to express both graphically and algebraically. The context includes attempts to analyze the inequality and find its roots.

Discussion Character

  • Homework-related, Exploratory, Technical explanation

Main Points Raised

  • One participant expresses difficulty in understanding how to represent a cubic non-linear inequality graphically and algebraically.
  • Another participant suggests that to express the equation graphically, one should simply plot it.
  • A further response recommends decomposing the cubic expression to find its zeros, noting that it may have up to three zeros and that the function can be analyzed over four intervals.
  • The same participant mentions that they have found that +1 and -1 are not roots and that the Rational Root Theorem is not applicable in this case.
  • A link to a method for solving cubic functions is provided, referencing Cardano's method.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there are differing views on how to approach the problem and the effectiveness of the suggested methods.

Contextual Notes

There are limitations in the discussion regarding the clarity of the inequality's direction and the specific cubic expression being analyzed. The applicability of the Rational Root Theorem is also questioned without resolution.

aew782
Messages
3
Reaction score
0
I just can't figure this out one question from my review test. I don't know hot to express it graphically or algebraically.
VlOaP.png
 
Mathematics news on Phys.org
I don't see any inequality.

As far as expressing the equation graphically, you just plot it.
 
aew782 said:
I just can't figure this out one question from my review test. I don't know hot to express it graphically or algebraically.
VlOaP.png

Try to decompose the cubic expression to find the zeros, meaning find if possible its linear and any quadratic factors (if quadratic factor cannot be factored further). It may have as many as three zeros, but not more. The function (now being equal to zero) is in possibly four intervals. You don't show us the direction of your inequality but you say you want to analyze the inequality; but anyway, you check the quality of the value of the "inequality" for each interval of the x-axis and determine if the x value is true for the inequality or false.

EDIT: harder than I thought. +1 is not a root and -1 is not a root. Rational Root theorem will not work.
 
Last edited:

Similar threads

Undergrad Violation of Bell Inequality with unentangled photons
  • · Replies 73 ·
3
Replies
73
Views
4K
MHB Solving Cubic Equation: x^3 - kx + (k + 11) = 0
  • · Replies 3 ·
Replies
3
Views
2K
Graduate Deriving an inequality from a paper
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Can Non-Linear Functions Be Converted to Linear Systems?
  • · Replies 10 ·
Replies
10
Views
2K
MHB Understanding Cubic Equation Formula for Polynomials of Degree Three
  • · Replies 9 ·
Replies
9
Views
4K
Undergrad Video on imaginary numbers and some queries
  • · Replies 3 ·
Replies
3
Views
2K
MHB Solving Inequality 4x-12≤6x+20
  • · Replies 1 ·
Replies
1
Views
2K
High School Can Multiple Outputs from a Single Input Help in Constructing Non-Linear Curves?
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Is e^pi a unique transcendental, or perhaps not transcendental?
  • · Replies 1 ·
Replies
1
Views
2K
Help with Time-Independent Perturbation Theory "Good" States Proof
  • · Replies 4 ·
Replies
4
Views
1K