SOLUTION: What is the simplest polynomial equation that can ce written that has roots -4 and 1 + 2i?
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Question 1038818: What is the simplest polynomial equation that can ce written that has roots -4 and 1 + 2i?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Complex roots always appear in conjugate pairs, so the simplest polynomial function with the given zeros also has 
as a zero. Hence, the simplest polynomial with the given roots is one of the third degree.
Therefore, your polynomial function has the following factors:
\ =\ (x\ +\ 4)\left(x\ -\ (1\ +\ 2i)\right)\left(x\ -\ (1\ -\ 2i)\right))
You can expand it for yourself. Hint: The product of two complex conjugates is the SUM of two squares.
John
My calculator said it, I believe it, that settles it
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