First, one important suggestion: Don't call your function as one Matlab function (roots, in fact is the one that you need to call).
After that, the equation (3) is trivial, you get the value of ere directly as you have in your function:
p = [0.23,0.25,0.27]'; % concentration of sample
er1 = (1+1.8*10^14*i); % Phase one Permittivity
er2 = (2.5+2.5*10^-3*i); % Phase two Permittivity
ereEQ3 = (1./4)*(((3*p-1)*er1) + ((2-3*p)*er2) + ((((3.*p-1)*er1) + ((2-3*p)*er2)).^2+8*er1*er2).^0.5);
For the other equation (2), yo need to obtain the roots of the second orden polynomial. One option is to use the roots function. (Note that you will obtain 2 solutions for each value of p, and only one is the same than the one obtained with the previous equation).
pol = [2+p*0, (-2+3*p)*er2 + (1-3*p)*er1, -er1*er2+p*0];
ereEQ2 = arrayfun(@(i) roots(pol(i,:)),1:numel(p),'uni',0);
