SOLUTION: Given that a function has zeros 3, -i and sqrt(4) and the function is degree 5, find the function.

Question 669892: Given that a function has zeros 3, -i and sqrt(4) and the function is degree 5, find the function.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

If

is a zero of a polynomial function, then

is a factor of the polynomial.

Complex zeros and irrational zeros come in conjugate pairs. That is if

is a zero, then

is also a zero. Also if

where

is rational and

is irrational is a zero, then

is also a zero.

Therefore four of the five factors of your desired polynomial function are:

Since

is not irrational, there is no guarantee that the conjugate is a zero. There is no way to determine the fifth zero from the information given and therefore there is no way to determine a unique 5th degree polynomial.

John

My calculator said it, I believe it, that settles it

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