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anonymous
 5 years ago
determine the roots of the given function
f(x)=x^54x^432x^3
anonymous
 5 years ago
determine the roots of the given function f(x)=x^54x^432x^3

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0The roots of a function are those values, x, such that f(x)=0. If you take a look at your function, you'll notice a common factor of x^3. Take this factor out to obtain, \[x^54x^432x^3=x^3(x^24x32)\]You can now go one step further to factor the quadratic you have to obtain,\[x^3(x^24x32)=x^3(x8)(x+4)\] The roots occur for those x such that\[x^3(x8)(x+4)=0\]This will be true when you get at least one of the factors equaling zero; that is\[x^3=0\rightarrow x=0\]\[(x8)=0\rightarrow x=8\]\[(x+4)=0\rightarrow x=4\]Your roots are\[x=0,8,4\]Hope this helps.
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