Use the given zero to find the remaining zeros of the function `f(x) = x^3 - 9x^2 + 4x - 36` ; zero:2i Enter the remaining zeros of f

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ishpiro eNotes educator| Certified Educator

If 2i is one zero of this function, then its conjugate, - 2i, is also zero of this function (this is because the function is a polynomial with real coefficients.)

This means, (x - 2i) and (x + 2i) are both factors of f(x).

 `(x - 2i)(x+2i) = x^2+ 4`

Divide f(x) by `x^2 +4` to find the remaining factor:

 See attached image for the long division problem that results in

x - 9.

Then, the last zero of the function is given by x - 9 = 0. It is 9.

The three zeroes of f(x) are 2i, - 2i and 9.



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