We have the equation $f(x)=x^3-7x^2 + 14x -6 $ .I have to find the root of the equation using bisection method in the interval of $]1.3 , 2 [$
First I find $f(1.3)=2.567 >0 $ and $f(2)=2>0$
I guess this means that based on the Intermediate Value Theorem the function isn't continuous and there isnt a $p∈]1.3 , 2[$ such that $f(p)=0$?
Anyway $a0=1.3$ and $b0=2$ ..we have $p0=a0+ [(b0-a0)/2]=1.65$ ...And we have $f(po)=2.53$,which is positive,same as $f(a0)$ and $f(b0)$.
This means$ a1=po=1.65$,$b1=bo=2$...and I should go on with the iterations,but I dont understand,for how long should I go on?