That is a good point, however I feel an even better solution in that case 
would be giving some of the roots and then giving some indication that 
there are an infinite number of roots. Disregarding the case where there 
are infinitely many roots, I don't see why it wouldn't be preferable to 
have the default behavior to be to give all the roots, or even just give 
the option to get all roots even if it is not the default. It just seems 
like useful functionality. What are the limitations towards implementing 
something like this? 

The Mathematica code was simply:
Solve[ Exp[-2*a*x]-4*a*x==0,x]//N



On Monday, March 5, 2018 at 5:14:05 PM UTC-6, vdelecroix wrote:
>
> On 05/03/2018 20:01, saad khalid wrote: 
> > Hello, and thank you for your response. While I agree that the behaviour 
> of 
> > the function certainly complies with the specifications listed in its 
> > description, I think everyone would agree that it would be better if it 
> did 
> > give all of the roots in a given interval. Would you happen to know 
> > anything about the difference between the alg Mathematica uses vs the 
> alg 
> > Sage uses that lets Mathematica find the root without making the 
> interval 
> > so precise? 
>
> Hello, 
>
> I don't agree. There might be infinitely many roots (just take 
> the function x * sin(1/x) in the interval [-1,1]). 
>
> There is a slight difference between root *isolation* and root 
> *approximation*. Since you are not providing the Mathematica code 
> you are using it is hard to tell anyway. 
>
> Best 
> Vincent 
>

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