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Two FindRoot questions


Hi,

These are not FindRoot questions, per se...

Here's a simple example which I want to ask three questions about:

f[k_] := x /. FindRoot[x^2 + k, {x, 0, 10}];
f[-10]
Plot[f[k], {k, -10, 10}]

First, I want the plot to only show where there exists a root.
Is the right solution to make f[] return Null?
How do I make f[] return Null? (Is there a way to "catch" the
warnings?)

Finally, I need to solve my equations to 20 digits. How do I do that?
I've read about Accuracy and Precision but it didn't help.

Thanks!


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