# False position method Calculator

## Calculates the root of the given equation f(x)=0 using False position method.

 Select a and b such that f(a) and f(b) have opposite signs, and find the x-intercept of the straight line connected by two points(a,f(a), (b, f(b)).This method converges more rapidly than the Bisection method.
f(x)
a
 , b f(a)f(b)≦0
 maximum repetition n 10 20 50 100 200 500
 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt
 $\normal False\ position\ method\\[10](1)\ initial\ value\qquad a_0,\ b_0\hspace{20}f(a_0)f(b_0)\le0\\[10](2)\ x_n={\large\frac{a_nf(b_n)-b_nf(a_n)}{f(b_n)-f(a_n)}}\\\hspace{25}f(x_n)\le\varepsilon\ \Rightarrow\ answer=x_n\\\hspace{25} a_{n+1}=x_n,\ b_{n+1}=b_n\hspace{20}f(a_n)f(x_n)\ge0\\\hspace{25} a_{n+1}=a_n,\ b_{n+1}=x_n\hspace{20}f(b_n)f(x_n)\ge0\\$

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