How Do You Solve a Cubic Polynomial with No Rational Roots?

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Homework Help Overview

The discussion revolves around solving a cubic polynomial, specifically the equation t³ + 2t² + 1 = 0. Participants express challenges in finding roots, particularly noting the absence of rational roots.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the difficulty of solving the polynomial by hand and question the validity of the equation presented. There is mention of using a graphing calculator as an alternative method, and some participants express uncertainty about the solvability of the polynomial without rational roots.

Discussion Status

The conversation is ongoing, with participants exploring different interpretations of the problem. Some have suggested that the polynomial may have irrational and complex roots, while others question the necessity of using the cubic formula. There is no explicit consensus on the approach to take.

Contextual Notes

Participants note that the polynomial cannot be solved using normal methods due to the lack of rational roots, and there is uncertainty regarding the requirements of the problem as posed in the textbook.

ThomasMagnus
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Hello,

I am trying to solve a degree three polynomial, but unfortunately I am stuck

t3+2t2+1=1

This is as far as I can get:
t(t2+2t)+1=0
Where do I go from here?

Thanks!
 
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I can get the solution by using my graphing calculator, but I would like to know how to do it by hand :)
 
Is the original problem t3+2t2+1=1

or t3+2t2+1=0 ??

You've written down two different things.
 
t3+2t2+1=0
sorry :)
 
It looks like this polynomial has one irrational root and two complex roots, so it can't be solved by hand (unless you know the cubic formula).
 
Yes, it cannot be solved using normal methods. There are no rational roots so synthetic division wouldn't work. Are you sure that it can be solved? Does the back of the book have the answer?

I've never used the cubic formula to solve a polynomial, and I doubt a textbook would require you to do that.
 

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