Solve a quadratic equation

So far I have solved the equation below with fsolve (with the help of this forum).

tau = 0.1
f4 = [3; 2; 6; 8]
f8 = [2; 6; 7; 3]
 eq = @(s,f4,f8) s*tau-(0.1.*s^2+3.54.*s-9.53).*f4.^2-f8;
 for f = 1:1:length (f4)
     F1 (f,:) = fsolve (@(s)eq(s,f4(f),f8(f)), 0);
end

Unfortunately, only a solution of the quadratic equation is given here. I didn't get along with the command roots () because my "formulas" were not accepted here. Does anyone have an idea here how elegantly all solutions can be found?

Answer 1

[Alex Mcaulley]

To use the function roots you need to reformulate your equation:

tau = 0.1
f4 = [3; 2; 6; 8]
f8 = [2; 6; 7; 3]

eq = @(f4,f8) [-0.1*f4^2, -3.54*f4^2 + tau,9.53*f4^2-f8];
sol = zeros(numel(f4),2);
for f = 1:1:length(f4)
    sol(f,:) = roots(eq(f4(f),f8(f)));
end

>> sol

sol =

  -37.7542    2.4654
  -37.3027    2.1527
  -37.8394    2.4672
  -37.8874    2.5030

[Mepe]

Works perfect. Thanks!