How do you find all the real and complex roots of #f(x) = x^3 - 4x^2 - 16x + 64#?

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Answer 1 · 2016-03-01T02:55:52

Use Grouping ...

#f(x) = x^3 - 4x^2 - 16x + 64#

#f(x) = (x^3 - 4x^2) - (16x - 64)#

Next, factor out common terms ...

#f(x) =x^2 (x - 4) - 16(x - 4)#

Simplify and set equal to zero ...

#f(x) =(x^2 - 16)(x - 4)=0#

Solve for x ...

#x^2-16=0#
#x=+-4#

#x-4=0#
#x=4#

So, the solutions are #x=4# or #x=-4# with #x=4# a double root .

Hope that helped

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