MATLAB: Solve a quadratic equation

equationrootssolve

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?

Best Answer

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
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