how to find the solution of third order polynomial symbolically?

Question

saravanakumar D 2017-5-24

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/341699-how-to-find-the-solution-of-third-order-polynomial-symbolically

评论： Walter Roberson 2017-5-25

采纳的回答： Walter Roberson

polynomial.jpg

在 MATLAB Online 中打开

this is my equation, where R is the only unknown

I want to solve this equation symbolically.my simplified polynomial equation becomes a*X^3+b*X+c=0, solve for X. a,b and c are functions of other variables. you can see from above image.

I tried below code

 syms R a c d
solve (a*R^3+c*R+d==0,R)

the solution came like below

 ans=
root(a*z^3 + c*z + d, z, 1)
 root(a*z^3 + c*z + d, z, 2)
 root(a*z^3 + c*z + d, z, 3)

Please anyone help me. I don't understand these results.

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Walter Roberson 2017-5-24

5
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/341699-how-to-find-the-solution-of-third-order-polynomial-symbolically#answer_268212

在 MATLAB Online 中打开

solve (a*R^3+c*R+d==0,R,'MaxDegree',3)

2 个评论
显示无隐藏无

saravanakumar D 2017-5-25

can you explains why "'MaxDegree',3" necessary here?

Walter Roberson 2017-5-25

https://www.mathworks.com/help/symbolic/solve.html#bue1gk5-3

"When you solve a higher order polynomial equation, the solver might use root to return the results. [...]

Try to get an explicit solution for such equations by calling the solver with MaxDegree. The option specifies the maximum degree of polynomials for which the solver tries to return explicit solutions. The default value is 2. Increasing this value, you can get explicit solutions for higher order polynomials."

In other words, the complete expression for a cubic root is long enough to be awkward, and is not usually explicitly needed, so it gets abbreviated. The complete expression for a quartic (degree 4) is very long and pretty much impossible to understand, so an abbreviation is used.

请先登录，再进行评论。