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

1. anonymous

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

thanx i got that