Question

Use the Bisection Method to locate all solutions of the following equations. Sketch the
function by using Matlab’s plot command and identify three intervals of length one that
contain a root. Then find the roots to six correct decimal places. (a) 2x3 − 6x − 1 = 0
(b) ex−2 + x3 − x = 0 (c) 1 + 5x − 6x3 − e2x = 0

**MUST BE DONE IN MATLAB AND NEEDS CODE

Answer 1

MATLAB CODE:

FUNCTION :

function [x, e] = MyBisectFunc (f,a1,b1,number)

format long

c1 = f(a1); d1 = f(b1);
if c1*d1 > 0.0
error ('Func has same sign at both endpoints .')
end

for i = 1:number

x = (a1 + b1 )/2;
y = f(x);
disp ([ x y])
if y == 0.0
e = 0;
break
end
if c*y < 0
b=x;
else
a=x;
end
end

x = (a1 + b1 )/2;
e = (b1-a1 )/2;

(a) 2x3 − 6x − 1 = 0:

MAIN FUNCTION

%f = @(x) exp(x)-2+x^3-x;
f = @(x) 2*x^3-6*x-1;
%f= @(x) 1+5*x-6*x^3-exp(2*x);
n=50;
a=-100;
b=100;
x = mybisect (f,a,b,n);
fprintf('x = %.6f\n',x);

output:

X=1.810038

(b) ex−2 + x3 − x = 0

MAIN FUNCTION:

f = @(x) exp(x)-2+x^3-x;
%f = @(x) 2*x^3-6*x-1;
%f= @(x) 1+5*x-6*x^3-exp(2*x);
n=50;
a=-100;
b=100;
x = mybisect (f,a,b,n);
fprintf('x = %.6f\n',x);

OUTPUT----

X=0.819432

(c) 1 + 5x − 6x3 − e2x = 0

MAIN FUNCTION:

%f = @(x) exp(x)-2+x^3-x;
%f = @(x) 2*x^3-6*x-1;
f= @(x) 1+5*x-6*x^3-exp(2*x);
n=50;
a=-100;
b=100;
x = mybisect (f,a,b,n);
fprintf('x = %.6f\n',x);

OUTPUT:

X=0.000000

PLOT FOR GRAPHS WITH THEIR INERVALS: