three order complex coefficient polynomial root matlab

2023 5 26
3 个回答
更新时间：2023 5 26
2 次查看（30 天）

0 个投票

Hi, I would like to find the root for a 3rd order polynomial with complex coefficient.
The polynomial is like:
28x^3 + Ax^2 + Bx - C = 0;
A,B,C are complex numbers.
I appreciate if anyone can help.

请先登录，再回答此问题。

回答（3 个）

Star Strider
Star Strider 2023-5-26
Ran in:

1 个投票

Ran in:
There are at least two options —
z = complex(randn(3,1), randn(3,1))
z =
0.1066 + 0.2511i 0.8599 + 2.0317i -0.2015 + 2.7642i
r = roots([28; z])
r =
0.4103 - 0.2811i -0.0640 + 0.4828i -0.3501 - 0.2106i
syms x
p = 28*x.^3 + z(1,:)*x.^2 + z(2,:)*x + z(3,:);
vpap = vpa(p, 5)
vpap = 
r = vpa(solve(p), 5)
r = 
.
John D'Errico
John D'Errico 2023-5-26

1 个投票

Another classic solution is to find the matrix that has the same eigenvalues as your polynomial has roots. Then use eig to compute the eigenvalues of this "companion matrix". This is in fact what roots does.
Walter Roberson
Walter Roberson 2023-5-26
Ran in:

1 个投票

Ran in:
syms x A B C
eqn = 28*x^3 + A*x^2 + B*x - C == 0;
solutions = solve(eqn, x, 'MaxDegree', 3)
solutions = 
char(solutions(1))
ans = '(C/56 + ((C/56 - A^3/592704 + (A*B)/4704)^2 + (B/84 - A^2/7056)^3)^(1/2) - A^3/592704 + (A*B)/4704)^(1/3) - (B/84 - A^2/7056)/(C/56 + ((C/56 - A^3/592704 + (A*B)/4704)^2 + (B/84 - A^2/7056)^3)^(1/2) - A^3/592704 + (A*B)/4704)^(1/3) - A/84'
char(solutions(2))
ans = '(B/84 - A^2/7056)/(2*(C/56 + ((C/56 - A^3/592704 + (A*B)/4704)^2 + (B/84 - A^2/7056)^3)^(1/2) - A^3/592704 + (A*B)/4704)^(1/3)) - A/84 - (C/56 + ((C/56 - A^3/592704 + (A*B)/4704)^2 + (B/84 - A^2/7056)^3)^(1/2) - A^3/592704 + (A*B)/4704)^(1/3)/2 - (3^(1/2)*((B/84 - A^2/7056)/(C/56 + ((C/56 - A^3/592704 + (A*B)/4704)^2 + (B/84 - A^2/7056)^3)^(1/2) - A^3/592704 + (A*B)/4704)^(1/3) + (C/56 + ((C/56 - A^3/592704 + (A*B)/4704)^2 + (B/84 - A^2/7056)^3)^(1/2) - A^3/592704 + (A*B)/4704)^(1/3))*1i)/2'
char(solutions(3))
ans = '(B/84 - A^2/7056)/(2*(C/56 + ((C/56 - A^3/592704 + (A*B)/4704)^2 + (B/84 - A^2/7056)^3)^(1/2) - A^3/592704 + (A*B)/4704)^(1/3)) - A/84 - (C/56 + ((C/56 - A^3/592704 + (A*B)/4704)^2 + (B/84 - A^2/7056)^3)^(1/2) - A^3/592704 + (A*B)/4704)^(1/3)/2 + (3^(1/2)*((B/84 - A^2/7056)/(C/56 + ((C/56 - A^3/592704 + (A*B)/4704)^2 + (B/84 - A^2/7056)^3)^(1/2) - A^3/592704 + (A*B)/4704)^(1/3) + (C/56 + ((C/56 - A^3/592704 + (A*B)/4704)^2 + (B/84 - A^2/7056)^3)^(1/2) - A^3/592704 + (A*B)/4704)^(1/3))*1i)/2'

类别

在 帮助中心 和 File Exchange 中查找有关 Polynomials 的更多信息

产品

标签

Community Treasure Hunt

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

Start Hunting!

Translated by