How do you find all the zeros of #x^3 + x^2 + 9x + 9 # given zero 3i?

1 Answer
George C.
May 21, 2016

The zeros are #-1#, #3i# and #-3i#.

Explanation:

We don't really need to be told that #3i# is a zero, except that it does inform us that we should include Complex zeros in the answer.

This cubic factors by grouping:

#x^3+x^2+9x+9#

#=(x^3+x^2)+(9x+9)#

#=x^2(x+1)+9(x+1)#

#=(x^2+9)(x+1)#

#=(x-3i)(x+3i)(x+1)#

So the zeros are #-1#, #3i# and #-3i#.

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