Can the Roots of x^4 + 7x^2 + 6 = 0 be Imaginary?

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Homework Help Overview

The discussion revolves around the polynomial equation x^4 + 7x^2 + 6 = 0, specifically examining the nature of its roots and whether they can be imaginary.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the substitution of t = x^2 to simplify the problem. There are questions regarding the nature of the solutions obtained and whether they align with the expectation of imaginary roots.

Discussion Status

Some participants have suggested methods for solving the equation, while others express confusion over the results, particularly regarding the nature of the roots. There is an ongoing examination of the calculations and assumptions made during the problem-solving process.

Contextual Notes

Participants are discussing the implications of obtaining real versus imaginary solutions and are questioning the validity of their calculations in light of the expected outcome.

Dustinsfl
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x^4 + 7x^2 + 6 =0

I know the answers are imaginary but I don't remember how to solve this equation.
 
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Let t=x^2 and solve for t. Then once you have t, you can easily find x.
 
If I do that and solve for t, I obtain two real solutions when all 4 all imaginary.
 
using quadratic formula:

[tex]x^2=\frac{-7\pm \sqrt{49-24}}{2}[/tex]
[tex]x^2=\{-6,-1\}[/tex]

both values of x^2 for negative, so all 4 values of x are imaginary. Check your working?
 

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