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.
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
(
