Finding roots of an exponential equation

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    Exponential Roots
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Homework Statement
Given that f(x)=(3^x).(e^x).(x^2-4) for real x.Find the root of the function.(setting f(x)=0).
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I know that both 3^x and e^x can't be 0 for real x. Then x^2-4=0 is the only choice and we get x=2,-2. Am I right? Or should I add something?
 
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