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anonymous

  • 5 years ago

determine the roots of the given function f(x)=x^5-4x^4-32x^3

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  1. anonymous
    • 5 years ago
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    The 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, \[x^5-4x^4-32x^3=x^3(x^2-4x-32)\]You can now go one step further to factor the quadratic you have to obtain,\[x^3(x^2-4x-32)=x^3(x-8)(x+4)\] The roots occur for those x such that\[x^3(x-8)(x+4)=0\]This will be true when you get at least one of the factors equaling zero; that is\[x^3=0\rightarrow x=0\]\[(x-8)=0\rightarrow x=8\]\[(x+4)=0\rightarrow x=-4\]Your roots are\[x=0,8,-4\]Hope this helps.

  2. anonymous
    • 5 years ago
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    thanx i got that

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