Solving for X (grph.calculator needed?)

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Homework Help Overview

The problem involves solving the cubic equation x³ + 2x² - 11x = 6. The original poster expresses difficulty in finding the zeros of the function due to a lack of access to a graphing calculator.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the inability to factor the equation into whole numbers and suggest using a graphing calculator to find the roots. The rational root theorem is mentioned as a potential approach, along with a reference to a more complex cubic formula.

Discussion Status

Some participants have offered guidance on potential methods to explore, including the rational root theorem and the cubic formula. There is acknowledgment of the challenges posed by the lack of a graphing calculator, and participants are exploring various interpretations of the problem.

Contextual Notes

The original poster notes that they will not have access to a graphing calculator until the school year starts, which affects their ability to solve the equation. There is also mention of the complexity of the cubic formula and the limitations of the rational root theorem in this case.

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Homework Statement


Solve For x: x3 + 2x2 - 11x = 6


Homework Equations


N/A


The Attempt at a Solution


I got to x3 + 2x2 - 11x - 6 = 0

It says to list the windows I work with (using a graphing calculator). I am unable to since I don't have one and won't be assigned one until the school year starts. How do I go about solving this function for zeros.
 
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This equation doesn't factor into whole numbers. :( Using the graphing calculator, you would graph it and then use the trace tool to find the roots. I believe there is a formula for cubic equations that is kind of like the quadratic equation but more complicated, but I don't know what it is.
 
Alright thank you. Will try and report back if I can :)
 
ArcanaNoir said:
This equation doesn't factor into whole numbers. :( Using the graphing calculator, you would graph it and then use the trace tool to find the roots. I believe there is a formula for cubic equations that is kind of like the quadratic equation but more complicated, but I don't know what it is.

gb7nash said:
Try the rational root theorem:

http://en.wikipedia.org/wiki/Rational_root_theorem

If that doesn't work and you can't use iterative methods (which probably won't give you exact roots), it's cubic formula for you.

I'm afraid the Rational root theorem doesn't work in this case.
And the formula for cubic equations is pretty messy:
http://en.wikipedia.org/wiki/Cubic_function

I'm afraid graphic calculator it is! :wink:
 

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