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Mr Davis 97
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I have the equation ##2t^{6} + 13t^{4} - 36 = 0##. How can I solve this for the real roots without using a CAS? That is, by hand?
Can a 6th degree equation be solved by hand without a CAS?
- Context: Undergrad
- Thread starter Mr Davis 97
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Discussion Overview
The discussion revolves around the problem of solving a 6th degree polynomial equation, specifically ##2t^{6} + 13t^{4} - 36 = 0##, for real roots without the aid of a computer algebra system (CAS). Participants explore various methods and strategies for tackling this equation by hand.
Discussion Character
- Exploratory, Technical explanation, Homework-related, Mathematical reasoning
Main Points Raised
- One participant suggests substituting ##u=t^2## to simplify the equation.
- Another participant proposes applying the rational root theorem after the substitution.
- A third participant provides a link to the rational root theorem for reference.
- It is also mentioned that graphing the equation could be a useful step after substitution.
Areas of Agreement / Disagreement
Participants present multiple approaches to solving the equation, but there is no consensus on a single method or solution path. The discussion remains open-ended with various strategies proposed.
Contextual Notes
The discussion does not address any specific limitations or assumptions regarding the methods suggested, nor does it resolve the mathematical steps involved in solving the equation.
Who May Find This Useful
This discussion may be useful for students or individuals interested in polynomial equations, particularly those looking for manual solving techniques without computational tools.
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