How to find roots of a quartic function with unknown constant coefficients?
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The polynomial is:
x^4 + 10.1ax^3 + 1.81x^2 + 9ax + 0.81 = 0
where a is an unkown constant coefficient.
I have to find the corresponding x values to further solve an ODE.
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Risposte (2)
James Tursa
il 28 Nov 2023
Modificato: James Tursa
il 28 Nov 2023
You can look here:
But the nature of the roots is going to depend on the value of a. Do you know anything at all about a? What is the context of the overall problem you are solving? What is the ODE?
Torsten
il 28 Nov 2023
Modificato: Torsten
il 28 Nov 2023
syms x a
p = x^4 + 10.1*a*x^3 + 1.81*x^2 + 9*a*x + 0.81;
sol = solve(p==0,'MaxDegree',4)
vpa(subs(sol,a,1)) % E.g. for a = 1
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Walter Roberson
il 29 Nov 2023
Modificato: Walter Roberson
il 29 Nov 2023
The roots get complicated and fragile
filename = fullfile(tempdir, 'sol.m');
addpath(tempdir);
syms x a
p = x^4 + 10.1*a*x^3 + 1.81*x^2 + 9*a*x + 0.81;
sol = solve(p==0);
solF = matlabFunction(sol, 'file', filename)
A = linspace(-1/2,1/2,200);
Y = cell2mat(arrayfun(solF, A, 'uniform', 0));
figure();
plot(A, real(Y(1,:)), A, real(Y(2,:)), A, real(Y(3,:)), A, real(Y(4,:)));
legend({'1 real', '2 real', '3 real', '4 real'})
figure();
plot(A, imag(Y(1,:)), A, imag(Y(2,:)), A, imag(Y(3,:)), A, imag(Y(4,:)));
legend({'1 imag', '2 imag', '3 imag', '4 imag'})
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