SOLUTION: How do I find the zeros of this problem? f(x)=x^3(4e^(4x))+3x^2*e^(4x) Thank you so much!!

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: How do I find the zeros of this problem? f(x)=x^3(4e^(4x))+3x^2*e^(4x) Thank you so much!!      Log On


   

Question 973037: How do I find the zeros of this problem?
f(x)=x^3(4e^(4x))+3x^2*e^(4x)
Thank you so much!!
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
Set equation=0
x%5E3%284e%5E%284x%29%29%2B3x%5E2%2Ae%5E%284x%29=0 factor out x%5E2e%5E%284x%29
%28x%5E2e%5E%284x%29%29%284x%2B3%29=0
x%5E2e%5E%284x%29=0 or 4x%2B3=0
.
Since e%5E%284x%29%29 is not zero (a number other than 0 raised to a power cannot equal 0), the first equation changes to x^2=0.
.
x%5E2=0 or 4x%2B3=0
+x=0 or x=-3%2F4