SOLUTION: Question is: Find a polynomial equation with integral coefficients that has the root 3 and 2i. I know that (x-3) is a factor of the root 3. 2i ??

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Question 467231: Question is: Find a polynomial equation with integral coefficients that has the root 3 and 2i.
I know that (x-3) is a factor of the root 3.
2i ??
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


is two times the imaginary number , defined as .

If the polynomial equation has the root , then it actually has the complex root . Remember that complex roots ALWAYS come in conjugate pairs, hence, if is a root, then so is

So the three factors of your polynomial are:

.

However, recall that the product of a pair of conjugates is the difference of two squares:



So:



You can FOIL it for yourself.

Note: This gives you the polynomial equation of least degree with integral coefficients that satisfies the condition that one of the roots is 3 and another root is . There are an infinity of others of greater degree.

John

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