Solve my determinant equal to zero with roots

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Hi!
I need help with solving for the roots of my polynomial im getting from my determinant of my matrices in a way where i dont have to collect the values manually in front of the variabel P from the determinant. Thanks in advance!
%%
clear all
clc
syms P
% Matrix definitions
KE_red =[13.0000 0 -8.4853;
0 13.0000 0;
-8.4853 0 8.0000];
KG_red =[ -(3*2^(1/2)*P)/65, 0, P/130;
0, -(3*2^(1/2)*P)/65, 0
P/130, 0, -(2*2^(1/2)*P)/195];
% Determinant
D=det(KE_red + KG_red)
% Solve for the roots of the determinant = 0
p = [-9*2^(1/2)/219700, 167/3380, -1328*2^(1/2)/195, 416];
r = roots(p)
[SL: formatted code as code. In the future please use the first button in the Code section of the toolstrip in the MATLAB Answers editor to create a section that formats code as code.]

Accepted Answer

Steven Lord
Steven Lord on 12 Feb 2024
You can use the vpasolve function to solve the polynomial, use the sym2poly function to automate extracting the vector of coefficients to a double precision vector, or use the coeffs function to automate extracting the vector of coefficients to a symbolic vector.
%%
syms P
sympref('FloatingPointOutput', false);
% Matrix definitions
KE_red =[13.0000 0 -8.4853;
0 13.0000 0;
-8.4853 0 8.0000];
KG_red =[ -(3*2^(1/2)*P)/65, 0, P/130;
0, -(3*2^(1/2)*P)/65, 0
P/130, 0, -(2*2^(1/2)*P)/195];
% Determinant
D=det(KE_red + KG_red)
D = 
% Solve for the roots of the determinant = 0
p = [-9*2^(1/2)/219700, 167/3380, -1328*2^(1/2)/195, 416];
r = roots(p)
r = 3x1
592.8693 199.1684 60.8116
s = vpasolve(D)
s = 
p2 = sym2poly(D)
p2 = 1x4
-0.0001 0.0494 -9.6311 415.9959
r2 = roots(p2)
r2 = 3x1
592.8696 199.1684 60.8110
p3 = coeffs(D, 'all') % Handle the case where one of the powers is not present
p3 = 
r3 = roots(p3)
r3 = 
To check, let's sort the various vectors. I'll use vpa to approximate the symbolic answers.
vpa([sort(r), sort(s), sort(r2), sort(r3)], 8)
ans = 
Those look to be in pretty close agreement.

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