Finding zeros of an equation

How do you find all zeros of an equation?

I have this problem and I'm suppose to find all the zeros of 3x^3 - 12x^2 - 33x + 80 over the range -10< x <10. I graphed it on my calculator and it clearly crosses the x-axis 3 times over -10 < x < 10.

When I do the problem in matlab it only gives me one of the zeros?

Any suggestions on how to find all the zeros?

Thank you.

[Steven]

Here is what I have so far:

function yzero = findzeros(range)

fun=@testfun;

[yzero,value]=fzero(fun,range);

%

function fx = testfun(x)

fx=(3.*x.^3)-(12.*x.^2)-(33.*x)+80;

end

end

Answer 1

[bym]

doc roots

[Steven]

I don't want to roots. I want to solve for all the zeros

Answer 2

[Wayne King]

   C = [3 -12 -33 80];
   Pzeros = roots(C);
   Pzeros

[Steven]

I'm asking to find all the zeros. which are when the points cross the x-axis at x=0. You're giving me the roots.

[Jared Jones]

the roots of the function are all the points where your function equals zero. fzero is mainly used for nonlinear functions.

Answer 3

[Wayne King]

Steven, In this case the roots are exactly the points you are looking for.

Please convince yourself:

   C = [3 -12 -33 80];
   Pzeros = roots(C);
   x = -10:0.01:10;
   y = 3*x.^3-12*x.^2-33*x+80;
   plot(x,y)
   grid on;
   hold on
   plot(Pzeros,zeros(length(Pzeros)),'r*','markersize',10);

[Steven]

Ok, thats how it looks on my graph. But how would I do this in terms of using a primary function and subfunction to compute the zeros and display the answers?

[Wayne King]

Write the primary function to accept the coefficients of the polynomial like the C vector above. Use roots() as a subfunction to find the zeros and then check the sign of the polynomial to the left and right of the zero, then you'll know whether it crosses the x-axis.

[Steven]

Here is what I have so far:

function yzero = findzeros(range)

fun=@testfun;

[yzero,value]=fzero(fun,range);

%

function fx = testfun(x)

fx=(3.*x.^3)-(12.*x.^2)-(33.*x)+80;

end

end

Then I typed this into the command window:

yzero = findzeros([-10, 10])

yzero =

5.1309

All I get is 1 zero. How do I get it to display all of them?

Answer 4

[bym]

if you insist on using a subfunction , consider the following:

function x = myroots(y)
% y is an integer range to find the roots in
n = y(1):y(2);
for k = 1:numel(n)
    fx=@(x)(3.*x.^3)-(12.*x.^2)-(33.*x)+80;
    r(k) = fzero(fx,k);
end
separate(r)
    function a = separate(r)
        a = sort(r(abs(diff(r))>10*eps));
    end
end

however it is sensitive to range given. Works for range[-10,10], other ranges may give different results

[Walter Roberson]

That's an example of a function that is a nested function but not a subfunction. To be a subfunction there would have to be a shared variable.