Can a Non-Integer Exponent be Used to Solve a Polynomial Equation?

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SUMMARY

The discussion centers on solving the polynomial equation B.x^b - x - A = 0, where A, B, and b are constants. It is established that if the exponent b is an integer not exceeding 4, algebraic solutions exist. However, when b is not an integer, as confirmed by the participants, numerical methods must be employed to find solutions. Thus, for non-integer exponents, numerical approximation techniques are essential for solving such equations.

PREREQUISITES
  • Understanding of polynomial equations and their structure
  • Familiarity with numerical methods for solving equations
  • Knowledge of algebraic solutions for polynomials
  • Basic grasp of constants and variables in mathematical expressions
NEXT STEPS
  • Research numerical methods for solving non-integer exponent equations
  • Explore software tools like MATLAB or Python's NumPy for numerical solutions
  • Learn about algebraic solutions for polynomials with integer exponents
  • Investigate the implications of non-integer exponents in polynomial equations
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Mathematicians, students studying algebra, and anyone involved in computational mathematics or numerical analysis will benefit from this discussion.

NY99
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Not sure if this is the right place but could somebody help me solve the following equation
B.x^b - x - A =0 wher A, B and b are constants.
Thanks
 
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NY99 said:
Not sure if this is the right place but could somebody help me solve the following equation
B.x^b - x - A =0 wher A, B and b are constants.
Thanks

Welcome on MHB NY99!...

... if b is integer not exceeding 4, then it exist a procedure for algebraic solutions ... otherwise generally the solutions have to be found numerically ... the same is if b is not an integer...

Kind regards

$\chi$ $\sigma$
 
Thanks for that. Unfortunately b is not an integer so I guess It will have to be numerically solved.
 

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