Polynomy (En)

28.11.2009 15:20

 

This program can be used for solving roots of polynomial equations with real coefficients, can compute any real or complex roots.

 

 Main features 
  • solving roots of polynomial equations with real coefficients, also shows multiplicity of roots
  • maximal supported degree of polynomial is 100
  • numerical error, | error | < 1E-5 (approximately 5 good numbers)
  • freeware under the terms of license


 

Examples
 

1. Example with quadratic polynomial equation: 

 

Let's say you need to know roots of this polynomial equation 2Z2 + 8Z - 5 = 0. Degree of polynomial is 2, so as very first step you must set it in window beside "n=" by writing the number 2. In the next steps you must set all coefficients with respect to their variables exponent. Coefficients are numbered from zero, so first (a0) coefficient is from first term with highest variable exponent (a0 Z2), so a0 koefficient value is 2.
Coefficients are all non zero and their values are 2, 8, -5.
To find roots of polynomial equation press "Solve" button. Roots will be showed in right list, and all results are automatically inserted to windows clipboard, so you can paste it by shift-insert keys anywhere (for example in notepad).

Polynomial, 2Z^2 + 8Z - 5 = 0

In first column are roots of polynomial, in second with "m" in header are multiplicity of roots. In this case are all roots of multiplicity 1.
But for example next polynomial equation Z2 + 2Z + 1 = 0 have one real root of multiplicity two, so in 2nd column is number 2.

Polynomial, Z^2 + 2Z + 1 = 0

Another example Z2 + 5Z + 9 = 0 have a pair of complex conjugate roots, both are roots of multiplicity 1. Character " i " in roots means complex variable (defined as i2 = -1).

Polynomal, Z^2 + 5Z + 9 = 0 

 

2. Example with cubic polynomial equation:


Let's say you need to know roots of this polynomial equation Z3 - 8Z2 + 15Z + 9 = 0. Degree of polynomial is 3, so as very first step you must set it in window beside "n=" by writing the number 3. In the next steps you must set all coefficients with respect to their variables exponent.
Coefficients are all non zero and their values are 1, -8, 15, 9.

Polynomial, Z^3 - 8Z^2 + 15Z + 9 = 0 

 

3. Example with polynomial equation of higher degree:


Let's say you need to know roots of this polynomial equation Z9 - 2Z8 + 6Z7 - 7Z6 + Z5 + Z4 + 2Z3 + 5Z2 + Z - 8 = 0. Degree of polynomial is 9, so as very first step you must set it in window beside "n=" by writing the number 9. In the next steps you must set all coefficients with respect to their variables exponent.
Coefficients are all non zero and their values are 1, -2, 6, -7, 1, 1, 2, 5, 1, -8.

Polynomial, Z^9 - 2Z^8 + 6Z^7 - 7Z^6 + Z^5 + Z^4 + 2Z^3 + 5Z^2 + Z - 8 = 0 
 

 

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