Question

MATLAR problem: Problem S: Determine the roots of f(x)=-12-21x+18r-2.75r with the methods of bisection, and false position. Please use initial guesses of x--1 and x-0, and a stopping criterion of 1%

Problem 5, using Matlab

Answer 1

Code:

clear all
clc
f = @(x) -12-(21*x)+(18*x^2)-(2.75*x^3);
a=-1;
b=0;
p=a;
%Bisection Method
while (abs(f(p))>0.01)
p = (a+b)/2;
if f(p) == 0
break;
end
if f(a)*f(p)<0
b=p;
else
a = p;
end
end
fprintf('The final root through bisection method is %f\n',p);

%False Position Method
p=a;
while (abs(f(p))>0.01)
p = (a*f(b)-b*f(a))/(f(b)-f(a));
if f(p) == 0
break;
end
if f(a)*f(p)<0
b=p;
else
a = p;
end
end
fprintf('The final root through False Position method is %f\n',p);

Editor CUsers\SANTOSH\Documents\MATLAB\bis.m* X EDITOR PUBLISH VIEW Find Files Insert E fxF Run Section Compare Comment % NAVIGATE New Оpen Save Breakpoints Run Run and Run and Advance Indent Print Time Advance FILE EDIT BREAKPOINTS RUN Haaland.m bis.m* X bisfalse.m cmp.m 2 clc f = @ (x) -12- (21*x) + (18*x^2) - (2.75*x^3); a-1 b-0 4 5- 6 р-а; Bisection Method 7 while (abs (f (p) ) >0. 01) 8 p(a+b)/2 if f (p) 0 break 10 11 12 end if f(a) f(p) <0 13 b-p 14 15 - else a p 16 17 end 18 end fprintf 'The final root through bisection me thod is f\n',p) 19 20 21 False Position Method 22 ра; while (abs (f (p) ) >0.01) p(a f(b) -b*f (a) ) / (f (b) -f (a)) 23 24 25 if f (p) == 0 break 26 end 27 28 if f(a) f(p)<o b-p 29 30 else 31 a p 32 end 33 end fprintfThe final root through False Position method is %f\n',p) 34 35 36 script Ln 27 Col 4

Output:

The final root through bisection method is -0.414551

p =

-0.4150

The final root through False Position method is -0.414689
>>

Command Window The final root through bisection method is -0.414551 -0.4150 The final root through False Position method is -0.414689

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Answer 2

-12 - 21x + 18x² - 2.75x³