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

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In summary, the conversation discusses solving an equation with constants A, B, and b, where b may or may not be an integer. It is mentioned that there is a procedure for algebraic solutions if b is an integer not exceeding 4, but otherwise the solutions will have to be found numerically.
  • #1
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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  • #2
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

$\chi$ $\sigma$
 
  • #3
Thanks for that. Unfortunately b is not an integer so I guess It will have to be numerically solved.
 

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

How do I solve a polynomial equation?

To solve a polynomial equation, you need to follow the steps of factoring, finding the zeros, and using the quadratic formula if necessary. You can also use online calculators or software programs to help you solve the equation.

What is the degree of a polynomial equation?

The degree of a polynomial equation is the highest exponent of the variable in the equation. For example, a polynomial equation with the term x^4 has a degree of 4.

Can all polynomial equations be solved?

Yes, all polynomial equations can be solved using various methods such as factoring, finding the zeros, or using the quadratic formula. However, some equations may have complex solutions or may require the use of advanced mathematical techniques.

How do I know if my solution to a polynomial equation is correct?

To check if your solution to a polynomial equation is correct, you can plug the values back into the original equation. If both sides of the equation are equal, then your solution is correct.

Are there any shortcuts or tricks for solving polynomial equations?

Yes, there are some shortcuts and tricks for solving certain types of polynomial equations. For example, the rule of signs can help you determine the number of positive and negative solutions, and the rational root theorem can help you find possible rational solutions. However, it is important to have a strong understanding of the basic methods to solve polynomial equations before using these shortcuts.

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