Find the roots of the equation

[dilraj]

I want to find first five roots of this equation using mathcad . I could'nt able to find any helpful info on the web, so i am posting it here

0.1*x+10*tan(0.1*x)=0

[ValeryOchkov · Accepted solution]

May be so

[ValeryOchkov]

Maple

[dilraj]

so, is it like u are taking different range to find root in that interval. How do we get to know we have just one root in 20-40 range or any other interval. Like from 20-40 it is giving me 28.6 , does that mean there is no root between 20-35 but there is one in 35-40. Hope u understand what i am trying to say. Thank you for explanation above @ValeryOchkov.

[-MFra-]

...firs six roots,,,,

[dilraj]

Thank you so much for your time and great method @-MFra-, but how do we guess x=28.6  initially. Like here u input initial value of x directly

[-MFra-]

Hi,

honestly, I took that value empirically, looking at the chart, which seems to me the quickest method. However, if you want to calculate it automatically, you might try applying the method used to initialize a root, that is, the method of the "Gershgorin" circle in the complex plane. If you are interested there are also complex roots, I believe.

[dilraj]

Hi,

I will look into that. Thank you for reply.

[ValeryOchkov]

See also

http://www.wolframalpha.com/input/?i=0.1*x%2B10*tan(0.1*x)%3D0