How would I do this? I know from the graph that the roots are -0.9 and 0.9 but how do I show this??? Any help much appreciated.

Thank you :)

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- Jan 13th 2010, 05:04 AMDBsHoShow that x^2*e^|x|=2 has two solutions
How would I do this? I know from the graph that the roots are -0.9 and 0.9 but how do I show this??? Any help much appreciated.

Thank you :) - Jan 13th 2010, 07:02 AMDinkydoe
If you may use that is continuous, it shouldn't be that hard: must reach all values in .

(look up theorem of Bolzano. I believe there's other even other names for that)

given that and it follows that there exists a with such that .

You can use this argument twice to show the existence of 2 roots (without necessarily finding them). - Jan 13th 2010, 07:12 AMDinkydoe
I meant the Intermediate value Theorem. It says: If f is contunious on a closed interval then for any exists a such that .