$$f(x)=x^4+2x^3+5x^2+5x-3$$ For this function, I used inverse quadratic interpolation and interestingly with 2 fixed points and 1 arbitrary, the algorithm always gave me the same result with the same number of iterations.
Two points I've chosen are: $(-1+2i, f(-1+2i)), (-0.5+2i, f(-0.5+2i))$
It does not matter what point you choose for the third one, it always gives you the same non-real root with the same number of iterations. Why does this happen? Is it because those two points are already close enough to the root?
Just realised that it gives the same root with different number of iterations if third point's $|x|$ is too small.