Concept

𝑚=𝑎+𝑏𝑎2

and if 𝑠𝑖𝑔𝑛(𝑓(𝑎))=𝑠𝑖𝑔𝑛(𝑓(𝑚)), 𝑎=𝑚 else 𝑏=𝑚

rate

it should has linear convergence rate since the interval cut half every iteration and 𝐶=0.5.