the eqn as you defined is a vector-value multi-variable function. fzero takes a scalar-value single-variable function.
so maybe you have a Writing error for eqn that make it vector value.
f = 0.35+0.1;
x0=f^2;
r = 0.3:0.3:1.5;
zeta = 0.25;
eps = 1/6;
eqn= @(A)(r.^4.*A.^2)-(2.*r.^2.*A.^2)-(2.*r.^2.*((3.*eps.*A.^4)./4))+(3.*((3.*eps.*A.^4)./4))+(((9.*eps.^2.*A.^6)./16))+(4.*zeta.*r.^2.*A.^2);
eqn(rand(1,5))
if you really want to solve the above system of equations you can use minimization functions like fminunc. or use solve for algebraic equations. ( you should change eqn for both of them)
for using fminunc the cost function should be a scalar value function. one easy method to change your eqn is taking norm from function:
eqn_= @(A)norm((r.^4.*A.^2)-(2.*r.^2.*A.^2)-(2.*r.^2.*((3.*eps.*A.^4)./4))+(3.*((3.*eps.*A.^4)./4))+(((9.*eps.^2.*A.^6)./16))+(4.*zeta.*r.^2.*A.^2));
x = fminunc(eqn_,ones(1,5));
x
Y=eqn(x)
norm(eqn(x))
