How do I solve for x in this equation?

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Homework Help Overview

The discussion revolves around solving the cubic equation -x^3 + 6x^2 - 11.998x + 8 = 0 for the variable x. Participants are exploring various methods and considerations related to this type of polynomial equation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss factoring as a potential method, with one noting the challenge of doing so. Others suggest using numerical methods like Newton's method, while some reference the rational root theorem to identify possible roots. There is also a mention of a formula for cubic equations and a question about the expected number of solutions.

Discussion Status

The discussion is active, with various methods being proposed and explored. Participants are questioning assumptions about the equation's roots and discussing the implications of the coefficients. There is no explicit consensus on a single approach, but several lines of reasoning are being examined.

Contextual Notes

Participants note that the equation's coefficients may influence the methods used to solve it, and there is uncertainty regarding the exactness of the given solution. The context of the course and expectations for solving cubic equations are also under consideration.

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Homework Statement


How can I calculate x in this equation: -x^3+6x^2-11.998x+8 = 0?


Homework Equations



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The Attempt at a Solution



**I tried factoring, but how??
**I know that the answer turns out to be x=2.16, but how did this come about?
 
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What course is this from? 2.6 is not an exact answer so maybe they want you to use Newton's method? There are a few ways of solving this-- but the method will depend on what course you are taking.
 
Hi Cuisine123! :smile:

(try using the X2 tag just above the Reply box :wink:)
Cuisine123 said:
How can I calculate x in this equation: -x^3+6x^2-11.998x+8 = 0?

It's a cubic, and you wouldn't be expected to know how to solve it in an exam.

(Basically, you put x = y + a so that the equation is of the form y3 + Ay + B = 0, and then use a formula)

Just use a calculator! :wink:​
 
By the "rational root theorem" the only possible roots are [itex]\pm 1[/itex], [itex]\pm 2[/itex], [itex]\pm 4[/itex], and [itex]\pm 8[/itex]. If that "11.998" were "12", then 2 would be triple root. As it is, however, that equation has no rational roots.
 
There is an analogous formula for polynomials of degree three: The solution of ax3+bx2+cx+d=0 is

cubic.gif
 
danielatha4 said:
The solution of ax3+bx2+cx+d=0 is …

shouldn't there be three solutions? :confused:
 

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