Borrar filtros
Borrar filtros

Matlab unable to find solution to cubic polynomial

3 visualizaciones (últimos 30 días)
Aleem Andrew
Aleem Andrew el 1 de Feb. de 2021
Editada: James Tursa el 1 de Feb. de 2021
The following cubic equation has three roots.
syms a
solve((1225*a)/2 - 6125 == ((2*a - 35)^2*(60*a + 4200))/840, a)
Matlab's output is:
root(z^3 + 35*z^2 - (8575*z)/2 + 42875, z, 1)
root(z^3 + 35*z^2 - (8575*z)/2 + 42875, z, 2)
root(z^3 + 35*z^2 - (8575*z)/2 + 42875, z, 3)
Can cubic equations like this be solved analytically in Matlab?

Respuesta aceptada

James Tursa
James Tursa el 1 de Feb. de 2021
Editada: James Tursa el 1 de Feb. de 2021
Tell the solve( ) function that the max degree of the polynomial is 3 to force explicit solutions for the result:
syms a
p = (1225*a)/2 - 6125 - ((2*a - 35)^2*(60*a + 4200))/840
solve(p,a,'MaxDegree',3)
which gives
ans =
28175/(18*(- 5187875/108 + (432^(1/2)*659937359375^(1/2)*1i)/432)^(1/3)) + ((432^(1/2)*659937359375^(1/2)*1i)/432 - 5187875/108)^(1/3) - 35/3
- 28175/(36*(- 5187875/108 + (432^(1/2)*659937359375^(1/2)*1i)/432)^(1/3)) - ((432^(1/2)*659937359375^(1/2)*1i)/432 - 5187875/108)^(1/3)/2 - (3^(1/2)*(28175/(18*(- 5187875/108 + (432^(1/2)*659937359375^(1/2)*1i)/432)^(1/3)) - ((432^(1/2)*659937359375^(1/2)*1i)/432 - 5187875/108)^(1/3))*1i)/2 - 35/3
- 28175/(36*(- 5187875/108 + (432^(1/2)*659937359375^(1/2)*1i)/432)^(1/3)) - ((432^(1/2)*659937359375^(1/2)*1i)/432 - 5187875/108)^(1/3)/2 + (3^(1/2)*(28175/(18*(- 5187875/108 + (432^(1/2)*659937359375^(1/2)*1i)/432)^(1/3)) - ((432^(1/2)*659937359375^(1/2)*1i)/432 - 5187875/108)^(1/3))*1i)/2 - 35/3
Then you can also note
>> simplify(ans)
ans =
(35*2^(1/3)*(- 121 - 1077^(1/2)*3i)^(1/3))/6 + (35*2^(1/3)*(- 121 + 1077^(1/2)*3i)^(1/3))/6 - 35/3
- (35*2^(1/3)*(- 121 + 1077^(1/2)*3i)^(1/3))/12 - (35*2^(1/3)*(1 + 3^(1/2)*1i)*(- 121 - 1077^(1/2)*3i)^(1/3))/12 + (2^(1/3)*3^(1/2)*(- 121 + 1077^(1/2)*3i)^(1/3)*35i)/12 - 35/3
- (35*2^(1/3)*(- 121 + 1077^(1/2)*3i)^(1/3))/12 + (35*2^(1/3)*(- 1 + 3^(1/2)*1i)*(- 121 - 1077^(1/2)*3i)^(1/3))/12 - (2^(1/3)*3^(1/2)*(- 121 + 1077^(1/2)*3i)^(1/3)*35i)/12 - 35/3
>> imag(ans)
ans =
0
0
0
So you can pick off the real part for the answer.

Más respuestas (0)

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by