Question

using matlab code please

5.2 Determine the real root of f(x) = 5x? - 5x2 + 6x-2: a. Graphically. b. Using bisection to locate the root. Employ initial guesses of x= 0 and xy = 1 and iterate until the estimated error &, falls below a level of Es = 10%.

Answer 1

clc;
clear all;

f=@(x)5*x^3-5*x^2+6*x-2; %function

disp('Root on interval [0 1]')
a=0;b=1; % interval

eps_step = 10/100;
n=1;
X(1)=a; %initial root;
err=1;
while (err>= eps_step && n~=100 )
  
c = (a + b)/2;
if ( f(c) == 0 )
break;
elseif ( f(a)*f(c) < 0 )
b = c;
else
a = c;
end
X(n+1)=c;
  
err=abs((X(n+1)-X(n))/X(n+1));

n=n+1;
end


disp('Solution by bisction method')
c
disp('Number of iteration')
n-1
disp('Realtive error')
err

%%%%%%%%%%%%%%%%%%%%%%%%%

Root on interval [0 1]
Solution by bisction method

c =

0.4063

Number of iteration

ans =

5

Realtive error

err =

0.0769

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