The algorithm given below describes the bisection method.

INPUT: endpoints a; b; tolerance TOL; maximum number of iterations N$0.$

OUTPUT: approximate solution p or message of failure.

$$ Step $1$: Set i $=1$;

FA $=$ f$($a$).$

$$ Step $2$: While i $<=$ N$0$ do Steps $2$:$1-2$:$4.$

$\{$ Step $2\mathrm{.}1$: Set p $=$ a $+($b $$ a$)=2$; $($Compute pi$.)$

FP $=$ f$($p$).$

$\{$ Step $2\mathrm{.}2$: If FP $=0$ or $($b $$ a$)=2<$ TOL then

OUTPUT $($p$)$; $($Procedure completed successfully.$)$

STOP.

$\{$ Step $2\mathrm{.}3$: Set i $=$ i $+1.$

$\{$ Step $2\mathrm{.}4$: If FA $$ FP $>0$ then set a $=$ p; $($Compute ai; bi$.)$

FA $=$ FP

else set b $=$ p$.$

$$ Step $3$ OUTPUT $($Method failed after N$0$ iterations, N$0=,$ N$0)$;

$($The procedure was unsuccessful.$)$

STOP.

Show the first three iterations for f$($x$)=$ x$25$x $+4$ and $[$a; b$]=[2$; $5]$ and

N$0=5,$ tolerance $"=103$