problem using 'Solve' (return only 1 solution)

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Marco Picillo on 22 May 2021
Commented: Marco Picillo on 23 May 2021
Hello,
I have a problem using solve for a symbolic expression (i'm using Matlab 2019a). I have a 3rd degree polynomial symbolic expression, and i want to find the roots.
I used:
[soluzione]=vpa(solve(equazione_gamma,CL,'Real',true))
and matlab returns:
soluzione =
0.047620242010553458040855966913202
But i expected 3 real solutions, in fact i tried using 'roots' and the solutions are:
p=[0.638 0.360 -0.860988 0.0401];
roots(p)
ans =
-1.4950e+00
8.8318e-01
4.7602e-02
(i approximated the coefficients). Seems that Matlab returns me only the last solution. What's the problem?
Thank you!

Andreas Apostolatos on 22 May 2021
Hi Marco,
It is not clear how you define expression 'equazione_gamma', but by reverse engineering your call to function 'roots', I believe that you define 'equazione_gamma' as '0.638*CL^3 + 0.360*CL^2 - 0.860988*CL + 0.0401' where 'CL' is a symbolic variable.
This way, the following script provides all three expected solutions in both MATLAB R2019a (both in general release and in Update 9) and MATLAB R2021a, namely,
syms CL;
equazione_gamma = 0.638*CL^3 + 0.360*CL^2 - 0.860988*CL + 0.0401;
[soluzione] = vpa(solve(equazione_gamma,CL,'Real',true))
soluzione =
0.047601767084402707714683600900841
0.8831762954368845400443443535789
-1.4950413854052997869439809325362
I hope this information helps.
Kind regards,
Andreas
Marco Picillo on 23 May 2021
thank you very much.

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