Finding Roots in the Equation x^4+x^3-4x^2-1=0

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SUMMARY

The equation x^4 + x^3 - 4x^2 - 1 = 0 does not have rational roots, as confirmed by multiple forum participants. The discussion suggests utilizing numerical approximation methods or consulting resources on quartic equations for solutions. The rational root test was mentioned as a potential starting point, but ultimately, the equation's complexity requires advanced techniques for resolution.

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Homework Statement



show that the equation x^4+x^3-4x^2-1=0

Homework Equations





The Attempt at a Solution


I wasn't sure where to start. The minus one at the end really threw me off. I tried to factor by grouping by coul;dn't figure out what to do with the -1
 
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Have you learned the rational root test?
 
ryan.1015 said:

Homework Statement



show that the equation x^4+x^3-4x^2-1=0

Homework Equations





The Attempt at a Solution


I wasn't sure where to start. The minus one at the end really threw me off. I tried to factor by grouping by coul;dn't figure out what to do with the -1

What's the rest of the sentence?
show that the equation x^4+x^3-4x^2-1=0

Show that this equation does what?

Please give us the exact wording of the problem.
 

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