Solve Polynomial Equation for Real a

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SUMMARY

The polynomial equation x10 + ax + 1 = 0 has a unique solution for real numbers a, specifically a = -2. This conclusion arises from the requirement that if r is a real solution, then 1/r must also be a solution. The discussion confirms that no other values of a satisfy this condition, establishing a definitive solution to the problem presented.

PREREQUISITES
  • Understanding of polynomial equations
  • Knowledge of real number properties
  • Familiarity with the concept of reciprocal solutions
  • Basic algebraic manipulation skills
NEXT STEPS
  • Explore polynomial root-finding techniques
  • Study properties of reciprocal functions in algebra
  • Investigate the implications of symmetry in polynomial equations
  • Learn about higher-degree polynomial behavior and solutions
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Mathematicians, students studying algebra, and anyone interested in solving complex polynomial equations.

Derivative86
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Hard problem...

Find all real numbers a with the property that the polynomial equation
x^10 + ax + 1 = 0
has a real solution r such that 1/r is also a solution
Thx for ur help :smile:
 
Last edited:
Mathematics news on Phys.org
Hmm!
i think i get a = -2 is the only solution.

-- AI
 

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