\(\normalsize False\ position\ method\\ (1)\ initial\ value a_0,\ b_0\hspace{20px}f(a_0)f(b_0)\le0\\ (2)\ x_n={\large\frac{a_nf(b_n)-b_nf(a_n)}{f(b_n)-f(a_n)}}\\ \hspace{25px}f(x_n)\le\varepsilon\ \Rightarrow\ answer=x_n\\ \hspace{25px} a_{n+1}=x_n,\ b_{n+1}=b_n\hspace{20px}f(a_n)f(x_n)\ge0\\ \hspace{25px} a_{n+1}=a_n,\ b_{n+1}=x_n\hspace{20px}f(b_n)f(x_n)\ge0\\ \) |
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