SOLUTION: I am trying to help my child with her homework. So, if you can explain it to me, maybe I can explain it to her.....without GIVING her the answer! Find all of the zeros of the f

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Question 267203: I am trying to help my child with her homework. So, if you can explain it to me, maybe I can explain it to her.....without GIVING her the answer!
Find all of the zeros of the function:

I know how to figure out how many positive and negative zeros, but I don't understand how to figure out how many imaginary zeros. Then I don't know how to find all of the zeros.
Answer by drk(1908) (Show Source):
You can put this solution on YOUR website!

first we use a technique called P-N-I This gives us the positive negative and imaginary zero combinations
P . . . N . . . I
3 . . . 1 . . . 0
1 . . . .1 . . . 2
So, I see that we must have 1 negative root somewhere.
Next I apply synthetic division to get roots.
-1 // 1 . . . . -15 . . . . 70 . . . . -70 . . . . -156
. . . . . . . . . . .-1 . . . . 16 . . . . .-86 . . . . 156
. . . . .1 . . . . .-16 . . . 86 . . . . .-156 . . . .0
and then
6// 1 . . . . -16 . . . . 86 . . . . -156
. . . . . . . . . . 6 . . . . -60 . . . .156
. . . . .1 . . . -10 . . . 26 . . . . .0
So we know that -1 and 6 are roots.
Now we can factor x^2 - 10x + 26 using the quadratic as

and then

which gives us imaginary answers of

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So, in total we have the following roots:
-6, 6, and 5 +-i