Solution of Equation "no real roots" result

Solution of Equation "no real roots" result - Solution of Equation "no real roots" result - Mensajes

#1 Publicado: 6/7/2022 16:26:55
Fog123

Fog123

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Hi, I have an polynomial equation (x^3 specifically) which I want to get the roots for. The roots are there if I plug in values from WolframAlpha (https://www.wolframalpha.com/input?i2d=true&i=-21.2Power%5Bx%2C3%5D%2B19707.8Power%5Bx%2C2%5D%2B6628342.5x-1125000000), I also checked on excel by changing x=? I found a root of x~128 but SMath won't do it.
On SMath it says no results even after I removed the unit and everything?
Question.jpg

I have used 'solve' function, but always get a "no real roots" message (see file attached).

Can someone help out?
Question.sm (14,04 KiB) descargado 1693 vez(es).


Many thanks in advance!
#2 Publicado: 6/7/2022 16:35:10
Alvaro

Alvaro

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Hi. Try solve(f(x),x,0,1500)=1223.
Best regards
Alvaro
#3 Publicado: 6/7/2022 17:12:34
overlord

overlord

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Try to plot these kind of functions to see what is going on.
Your function is equals to zero around 1200.
Here is your solution with various solvers.

Regards

Question_answer.sm (21,25 KiB) descargado 1684 vez(es).

2022-07-06_23-10.png
#4 Publicado: 6/7/2022 18:49:02
Jean Giraud

Jean Giraud

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Wrote

I have an polynomial equation ... which I want to get the roots for.


Your polynomial is doctored in yellow.
By inspection, the plot reveals complex roots, i.e: 2 complex roots.
Comment: respect preciously the Lagrange canonical order.
Cheers ... Jean.

Question Doctored.sm (29,25 KiB) descargado 1748 vez(es).

#5 Publicado: 6/7/2022 21:58:06
overlord

overlord

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Here is your complete answer by the way.
Good old maple saves the day again.

Regards

2022-07-07_03-54.png
#6 Publicado: 7/7/2022 7:59:06
Jean Giraud

Jean Giraud

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As it looks, if you create cubic at profusion,
the cubic roots solver will be a great companion.
It comes useful in PID techniques.
Polyroots is native in Smath.

Polyroots.PNG
#7 Publicado: 7/7/2022 8:38:23
Jean Giraud

Jean Giraud

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... once your cubic in hand,
you can solve for a specific datum.
Cheers ... Jean.

Solve Datum.PNG
#8 Publicado: 11/7/2022 11:24:19
Fog123

Fog123

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Hi Everyone,

Thank you for your replies they were very helpful. I really appreciate the people who went above and beyond to explain the various ways of getting the roots and even changing the datum.
It proved extremely helpful to plot the function where I quickly realized the difference between my SMath and WolframAlpha results. The 4th term 'x4' or 'c' is supposed to be a negative.
I though I was doing something wrong with inputting the data into SMath, but it was the function which I was inputting that was wrong.

In my program by changing "Qd" to a (negative) I got the following roots.
Question_finished.JPG

Lesson learned: Quadruple check your functions.

Question_finished.sm (21,5 KiB) descargado 1661 vez(es).
#9 Publicado: 11/7/2022 13:10:43
Jean Giraud

Jean Giraud

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Good job ! Start be friend with Lagrange canonic.

Question_finished Canonic Lagrange.sm (27,67 KiB) descargado 1671 vez(es).
#10 Publicado: 11/7/2022 13:32:16
Jean Giraud

Jean Giraud

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... read more in pink.
Cheers ... Jean.

Question_finished Canonic Lagrange.sm (33,2 KiB) descargado 1672 vez(es).
#11 Publicado: 11/7/2022 14:05:45
overlord

overlord

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