Find all zeros of quartic function

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SUMMARY

The discussion centers on finding all zeros of the quartic function defined by the equation f(x) = x^4 - x^3 - 5x^2 - x - 6. Participants emphasize the importance of showing the work involved in solving the equation rather than simply providing the answer. The community encourages users to share their attempts and specific points of confusion to receive targeted assistance in solving the problem.

PREREQUISITES
  • Understanding of quartic functions and their properties
  • Familiarity with polynomial equations and their roots
  • Knowledge of factoring techniques and the Rational Root Theorem
  • Basic skills in algebraic manipulation and equation solving
NEXT STEPS
  • Study the Rational Root Theorem for identifying potential rational roots of polynomials
  • Learn techniques for factoring quartic equations
  • Explore synthetic division as a method for finding polynomial zeros
  • Investigate numerical methods for approximating roots of higher-degree polynomials
USEFUL FOR

Students studying algebra, mathematics educators, and anyone seeking to improve their skills in solving polynomial equations, particularly quartic functions.

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Homework Statement



Need help finding all zeros of this quartic function. Can someone show the work involved in solving the following equation?

Homework Equations



f(x)=x^4-x^3-5x^2-x-6

The Attempt at a Solution

 
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Sorry, that's not how it works here. We won't just do the work for you, if you post what you have done and where you are stuck then we can give you some guidance as to how to proceed.
 

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