Factorizing polynomial of degree 4

[Pokemon]

Could anyone tell me how to find the roots of the following equation
m^4-8m^2+m+12

 

[Deleted member 4993]

Could anyone tell me how to find the roots of the following equation
m^4-8m^2+m+12

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Please share your work/thoughts about this assignment.

Using rational root theorem you can show that this polynomial does not have a rational root.

What other method can be applied to estimate the "irrational" real roots - if they exist?

 

[JeffM]

Could anyone tell me how to find the roots of the following equation
m^4-8m^2+m+12

What has your teacher taught you about depressed quartics?

 

[Steven G]

Could anyone tell me how to find the roots of the following equation
m^4-8m^2+m+12

The answer to your question is no.
If on the other hand you had asked could anyone help me find the roots of the following equation, that would be an entirely different question.
Can you tell us where you are stuck? Can we see your work so we know how you want to do this problem and see where you are making a mistake?

 

[Steven G]

I would 1st try the rational root theorem

 

[topsquark]

Could anyone tell me how to find the roots of the following equation
m^4-8m^2+m+12

Try this. It's a bit hairy but it can work. We know that a quartic can always be factored into two quadratic factors:
[math]m^4 - 8m^2 + m + 12 = (m^2 + am + b)(m^2 + cm + d)[/math]
Multiply things out and match coefficients. After some work you will find that [math]m^4 - 8m^2 + m + 12 = (m^2 - m - 3)(m^2 + m - 4)[/math].

-Dan

 

[Pokemon]

Try this. It's a bit hairy but it can work. We know that a quartic can always be factored into two quadratic factors:
[math]m^4 - 8m^2 + m + 12 = (m^2 + am + b)(m^2 + cm + d)[/math]
Multiply things out and match coefficients. After some work you will find that [math]m^4 - 8m^2 + m + 12 = (m^2 - m - 3)(m^2 + m - 4)[/math].

-Dan

Thank you ...