plot all roots of a polynomial which has a interval coefficient

For example, if the polynomial is: p= s^3 + a*s^2 + s + 1 which a=[2,3].

How can plot all the roots of this polynpomial? I can only figure out the roots when 'a' is fixed.

[Rik]

Wouldn't that just mean you would have to find the roots in a loop? There is an analytical way to determine the roots, but that will be a pain to implement.

[senhan yao]

Yeah,it seems very laborious. I can plot the roots when 'a' is fixed. I think maybe there is a method like below to solve this problem.

P=[1 2 1 1];
z=roots(p);
scatter(real(z),imag(z));

Answer 1

[Rik]

I meant something like this.

N=200;
Z=NaN(N,3);
a=linspace(2,3,N);
for n=1:numel(a)
    p=[1 a(n) 1 1];
    z=roots(p);
    Z(n,1:numel(z))=z;
end
h=plot(real(Z),imag(Z));
legend({'1','2','3'},'Location','NorthWest')
[h.Color]=deal('b','r','k');

[senhan yao]

This is what i want ! It works! Thank you!