finding roots of the equation

For several value of n (n=1,2,3,4,...), it was needed to find roots of under equation.

f(n,I)=n*210+(I^2/n)*[(((200-32I)^2)/200)+32]-197

Please help me, how can I find answer by using MATLAB. And please give me answers (value of I) for n=1,2,3,4,5

Answer 1

[Matt Tearle]

You may want to check your function, because it doesn't seem to have any (real) zeros:

f = @(n,I) n*210+(I.^2/n).*((((200-32*I).^2)/200)+32)-197;
figure
I = linspace(-100,100,5001);
y = f(1,I);
plot(I,y)
min(y)

But, the approach would be to define a function handle for f, as above, then set the value of n and apply fzero to the resulting function of one variable ( I ):

f = @(n,I) n*210+(I.^2/n).*((((200-32*I).^2)/200)+32)-197;
I0 = 0; % Make an initial guess
for n = 1:5
  g = @(I) f(n,I);  % Make a new function from f(n,I) with n fixed
  I0 = fzero(g,I0)  % Find zero, starting with previous result
end

[Walter Roberson]

The real roots occur only for n <= 197 / 210

[mohammad]

thanks let me check