How do you find all the zeros of #f(x)=x^3 +6x^2 - 6x-36#?

1 Answer
sente
Mar 5, 2016

Factor #f(x)# to see that the zeroes occur at #-6#, #sqrt(6)#, and #-sqrt(6)#

Explanation:

Using the technique of factoring by grouping as well as the difference of squares formula , we can factor #f(x)# as

#x^3+6x^2-6x-36 = x^2(x+6)-6(x+6)#

#=(x^2-6)(x+6)#

#=(x+sqrt(6))(x-sqrt(6))(x+6)#

In its factored form, we can see that the zeros occur when any of the factors become #0#, that is, when #x=-6# or #x=+-sqrt(6)#.

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