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Marius_P10-Marble
10-Marble
January 23, 2023
Solved

solve of equation with combination of coefficients

  • January 23, 2023
  • 2 replies
  • 3289 views

Hello,

I would like to know if you could help me please with some idea how could I solve the following 3rd degree equation:

- equation is of type ax^3+bx^2+cx+d=0

- each of the coefficients has a max and min value:

    • a ->(amin, amax)
    • b -> (bmin, bmax)
    • c-> (cmin, cmax)
    • d-> (dmin, dmax)

It results a high number of 3rd equations to be solved from all the possible combinations of the min and max values of the coefficients.

Solving each combination in part takes lot of time, so I would like to know if there is any possible way to get the solutions from all the equations obtained from all the possible combinations of coefficients?

Thank you,

Marius 

 

 

 

 

 

 

Best answer by Werner_E

Yes, you are right.  I used the order used by polyroots which is coefficient of x^0 as first value.

Werner_E_0-1674520775799.png

Actually I hadn't noticed that thats differently from the function definition the IP used in his question.

 

If thats an issue it can easily be changed

Werner_E_1-1674521275470.png

 

2 replies

A
AlanStevens19-Tanzanite
19-Tanzanite
January 23, 2023

Here's one way:

 

polyroots.png

Alan

(the attached file is M15 format)

W
Werner_E25-Diamond I
25-Diamond I
January 23, 2023

> get the solutions from all the equations

ALL equations? For sure?

There is an infinite(!) number of possible coefficients "a" from amin to amax and the same goes for b, c and d.

Every equation will have 3 solutions. So you have to expect 3*infinity^4 values. No matter which method you may chose to calculate them, it will take infinity time and if you are using Prime it even may take much longer 😉

So maybe you may reconsider what you really are looking for.

A
AlanStevens19-Tanzanite
19-Tanzanite
January 23, 2023

I took the question as meaning just use the two extreme values for each coefficient.  Of course, if the requirement is for all values in between the extremes, then, as you say, there is an infinite number of possible solutions!

 

Alan

M
Marius_P10-MarbleAuthor
10-Marble
January 23, 2023

No, my question is referring only to the max & min values of each coefficient. I am using PTC Mathcad Prime 7 for worst case calculations.

Could you tell me please how to build the matrix of coefficients?

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