how do i find the roots of this function? the function is attached

x=-10:1:10;
y=x.^3-x.^2+5.*x.*sin((pi().*x)/4-(pi()*5)/4)+3;
y1=0;
plot(x,y,x,y1)      
xlabel('x'); grid on
ylabel('y')

Answer 1

[Azzi Abdelmalek]

syms x
y=x^3-x^2+5*x*sin(pi*x/4-5*pi/4)+3
solve(y)

To find all the roots, you can use fsolve

y=@(x) x^3-x^2+5*x*sin(pi*x/4-5*pi/4)+3
x0=-0.5   % first starting point
x1=fsolve(y,x0)
x0=2   % second starting point
x2=fsolve(y,x0)

[Sebastian Arias]

i do not have the symbolic math toolbox is there another way to do this?

[Sebastian Arias]

i do not have any add-ons to matlab. just the base student edition. for the fsolve i need optimization toolbox

Answer 2

[Torsten]

Plot the function and use "fzero" to determine the roots with appropriate starting intervals taken from your graphical inspection.

Best wishes

Torsten.