It might if you aske it to and give it a causal system it can work with —
s = tf('s');
eqn = @(u) 1 / (1472*s^4 - 99.2*s^3 -256*s^2*u.^2 + 1393*s^2 + 2.4*s*u^2 - 25*s -24*u^2 + 150)
u = 1;
figure
rlocus(eqn(u))
grid
u = 10;
figure
rlocus(eqn(u))
grid
eqn = @(s,u) 1472.*s.^4 - 99.2.*s.^3 -256.*s.^2.*u.^2 + 1393.*s.^2 + 2.4.*s.*u.^2 - 25.*s -24.*u.^2 + 150;
figure
fimplicit(eqn, [[-1 1]*10 [-1 1]*10])
grid
I would not consider that to be a root locus plot, however that is likely the only way to work with it as originally stated.
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