How to solve for multiple roots

Hello, I am trying to solve the first 500 roots of the following equation tan (x)= (3x)/(3+(60.5*(x^2)) But I cannot figure out how to do it. Any help will be appreciated.

Answer 1

[John D'Errico]

The first 500 roots? Why 500? Are there 500 such roots?

By the way, I think you need to learn to use fewer parens.

f = @(x) tan(x) - 3*x./(3+60.5*x.^2);

One root clearly lies at x == 0. In fact, quick examination suggests that n*pi is a good approximation to all non-negative roots.

f(pi*(0:10))
ans =
          0    -0.015705   -0.0078821   -0.0052584   -0.0039448   -0.0031562   -0.0026303   -0.0022546   -0.0019728   -0.0017537   -0.0015783

So just use a loop, calling fzero for each starting value n*pi.

xn = zeros(1,11);
for n = 1:10;
  xn(n+1) = fzero(f,n*pi);
end

xn
xn =
  Columns 1 through 7
                         0          3.15721947602233          6.29105738669815          9.43003337009966           12.570314108792          15.7111187818028          18.8521858417768
  Columns 8 through 11
          21.9934029606895           25.134713911635          28.2760874364729          31.4175047721421

ezplot(f,[0,35])
hold on
refline(0,0)
plot(xn,0,'ro')

Answer 2

[madhan ravi]

syms x
e1=tan(x)==(3*x)/(3+(60.5*(x^2)))

vpasolve(e1,x,1)

[madhan ravi]

For multiple roots you have to specify the interval

Answer 3

[Bambatta]

Thank you So much John and Ravi

[madhan ravi]

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