Solving equations in a given range

[Jan 11]

I solve the equation TAN (3x) = - x ^ 2 + 3.
The calculator gives six solutions in the range {-3,633 to 2,695}. OKAY. When we set the range of solutions in the range x = 0 to 10, he will give all the solutions correctly. OKAY. Next, when we set x = 10 to 15, it will give only two solutions. However, there are 4 solutions. Now I set the range x = 25 to 30. HP Prime finds no solution. There are as many as 5 solutions in this range.
I checked how the TI-Nspire CX II-T calculator does it. I do all the examples great, perfectly. See this in the attached screenshots of both calculators.


       

[parisse]

That's because the default step for the bisection solver is too large to detect the roots. You can obtain more solutions by adding an optional argument, like this
solve(tan(3x)=-x^2+3,x=10..15,xstep=0.001)
or
solve(tan(3x)=-x^2+3,x=25..30,10000)

[Jan 11]

Dear Parisse. Thank you very much for very valuable advice. I've never heard of it. Great, all equations have been solved. Thank you again.

[parisse]

I have just increased the default number of steps, this will detect more solutions if the optional argument is not given.