Solution of Equation "no real roots" result

#1 Pubblicato: 06/07/2022 16:26:55

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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?

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) scaricato 1697 volta(e).

Many thanks in advance!

#2 Pubblicato: 06/07/2022 16:35:10

Alvaro

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Hi. Try solve(f(x),x,0,1500)=1223.
Best regards
Alvaro

#3 Pubblicato: 06/07/2022 17:12:34

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) scaricato 1685 volta(e).

#4 Pubblicato: 06/07/2022 18:49:02

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) scaricato 1751 volta(e).

#5 Pubblicato: 06/07/2022 21:58:06

overlord

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

Regards

#6 Pubblicato: 07/07/2022 07:59:06

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.

#7 Pubblicato: 07/07/2022 08:38:23

Jean Giraud

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

#8 Pubblicato: 11/07/2022 11:24:19

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.

Lesson learned: Quadruple check your functions.

Question_finished.sm (21,5 KiB) scaricato 1663 volta(e).

#9 Pubblicato: 11/07/2022 13:10:43

Jean Giraud

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Good job ! Start be friend with Lagrange canonic.

Question_finished Canonic Lagrange.sm (27,67 KiB) scaricato 1673 volta(e).

#10 Pubblicato: 11/07/2022 13:32:16

Jean Giraud

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

Question_finished Canonic Lagrange.sm (33,2 KiB) scaricato 1676 volta(e).

#11 Pubblicato: 11/07/2022 14:05:45

overlord

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