SOLUTION: a polynomial with a real coeficients that has a complex imaginary sero 2i?

Question 465666: a polynomial with a real coeficients that has a complex imaginary sero 2i?
Found 2 solutions by tinbar, solver91311:
Answer by tinbar(133) (Show Source): You can put this solution on YOUR website!
f(x) = a(x-2i) where a is a Real number
There's an infinite amount of answers to this question, just see what conditions my example satisfies and make your own.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The actual complex number for the given zero is , but we know that complex roots ALWAYS come in conjugate pairs, which is to say if is a root, then is also a root -- guaranteed.

So our required polynomial has at least three factors, some constant and then the two complex factors: and

A little FOIL keeping in mind that and the distributive property gets us to:

which is the family of polynomial functions of least degree that have as a zero.

John

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

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