SOLUTION: Hi I'm having trouble understanding. Finding all zero's of a polynomial function given one zero. My problem is: f(x)= x^4-32x^2-144; one zero is -2i The answer given is, 2i,6,-6

Question 670349: Hi I'm having trouble understanding. Finding all zero's of a polynomial function given one zero. My problem is: f(x)= x^4-32x^2-144; one zero is -2i
The answer given is, 2i,6,-6 but I'm not understanding how. Thank you!
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
To find the zeros of this polynomial function we need to set equal to and factor the equation.
....since you are given one zero which is , it is result of the square of negative number that could be only ; only gives you root , as as well
therefore, you are actually given two roots, and now we will find remaining two
.....replace with
.....group
...factor out from the first group and from the second group

Now we set each factor to zero:
............... .........=> given roots: the imaginary numbers and
..........................real root
......................real root

show it on a graph:

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