SOLUTION: Hello! I need help solving this: I have the function:f(x) = 4x^3 + 5x^2 + 36x + 45 and the zero: 3i I have to use the given zero to find all the zeros of the function. T

Question 977052: Hello!
I need help solving this:
I have the function:f(x) = 4x^3 + 5x^2 + 36x + 45
and the zero: 3i
I have to use the given zero to find all the zeros of the function.
Thank you
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
Since it has rational coefficients, the complex conjugate of is also a root.
So is a factor of f(x).
Divide the factor from the polynomial to find the remaining factor.

You know that is the leading term of the factor because of the leading term in f(x).

Which leaves,

Then the constant term of the factor would be since,

So the remaining factor is,

So the zeros are 3i,-3i, and -5/4.
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