# Given that the polynomial function (below) has the given zero, find the other zeros? #f(x) = x^4 - 5x^3 + 7x^2 - 5x + 6; -i#

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I know the answers are #i, 2, 3# but I don't know how to find them.

I know the answers are

##### 1 Answer

The general factored form of a quartic equation is:

Where

#### Explanation:

Given:

We can substitute

Because all of the coefficients are real, we know that imaginary roots must exist in conjugate pairs, therefore,

Because the leading coefficient of the given equation is 1, we know that

We know that

The roots are: