Re: NSolve unable to find all possible roots

*To*: mathgroup at smc.vnet.net*Subject*: [mg115597] Re: NSolve unable to find all possible roots*From*: Peter Pein <petsie at dordos.net>*Date*: Sun, 16 Jan 2011 05:51:17 -0500 (EST)*References*: <igrqbc$qn2$1@smc.vnet.net>

On 15.01.2011 10:45, Luiz Melo wrote: > Dear mathgroup, > The equation below has three possible roots, namely: 0., 1.99, -1.99. > > eq = x*(Sqrt[-13.319 - x^2] + 2.41*Sqrt[1.004 - x^2]) > > If we try NSolve[eq == 0, x], we get {{kx-> 0.}} only. > > How to instruct NSolve to search for the other two roots of the above equation? > > Thank you > Luiz Melo > > -- > > Hi Luiz, your expression has got exactly one root at x=0. Obvously you did not try: In[1]:= expr = x*(Sqrt[-13.319 - x^2] + 2.41*Sqrt[1.004 - x^2]); Table[expr, {x, {-1.99, 0, 1.99}}] Out[2]= {0. - 16.5178 I, 0. + 0. I, 0. + 16.5178 I} maybe there' s just a typo (subtract the squareroots): In[3]:= expr2 = x*(Sqrt[-13.319 - x^2] - 2.41*Sqrt[1.004 - x^2]); Table[expr2, {x, {-1.99, 0, 1.99}}] Out[4]= {0. - 0.0263184 I, 0. + 0. I, 0. + 0.0263184 I} comes at least near zero. So lets try to solve the equation expr2 = 0 using NSolve : In[5]:= NSolve[expr2 == 0] Out[5]= {{x -> 1.99573}, {x -> -1.99573}, {x -> 0.}} is this the expected result? Cheers, Peter