Plotting with bisection method

I have this so far:

clc;
xlabel('x')
ylabel('f(x)')
title('Roots of f(x)= -x^4+12x^2-3x-5')
fx= @(x) -x.^4+12*x.^2-3*x-5;
tol= 10^-10;
a=0;
b=1;
while 1
    
    c=(a+b)/2;
    if abs(fx(c)) <= tol
        fprintf('foud the root at x= %f\n', c);
        break;
    end
    if fx(a)*fx(c)<0
        b=c;
    else
        a=c;
    end
end

xx= -4:.1:4;
plot(xx,fx(xx),'b-');
grid on;
hold on;
plot(c,fx(c),'r*', 'Markersize', 10);
xlabel('x')
ylabel('f(x)')
title('Roots of f(x)= -x^4+12x^2-3x-5')

Need help getting to this:

Answer 1

[Chunru]

Bisection method tries to find solution in a given interval. Generally, you don't know how many roots a non-linear equation has and where the roots are. So it might be an guess and check problem. For your problem, you can plot the curve and estimate where the roots are roughly located.

clc;
xlabel('x')
ylabel('f(x)')
title('Roots of f(x)= -x^4+12x^2-3x-5')
fx= @(x) -x.^4+12*x.^2-3*x-5;
tol= 10^-10;
% intervals of all roots
aa = [-4 -2 0 2];
bb = [-2  0 2 4];

xx= -4:.1:4;
plot(xx,fx(xx),'b-');

xlabel('x')
ylabel('f(x)')
title('Roots of f(x)= -x^4+12x^2-3x-5')
grid on;

hold on;

for i_interval = 1:length(aa)
    a=aa(i_interval);
    b=bb(i_interval);
    while 1
        
        c=(a+b)/2;
        if abs(fx(c)) <= tol
            fprintf('foud the root at x= %f\n', c);
            break;
        end
        if fx(a)*fx(c)<0
            b=c;
        else
            a=c;
        end
    end
    plot(c,fx(c),'r*', 'Markersize', 10);
end

foud the root at x= -3.528261
foud the root at x= -0.537768
foud the root at x= 0.809110
foud the root at x= 3.256919