SOLUTION: A polynomial g(x) of degree 5 whose coefficients are real numbers has zeros 2, 3, -3, and 7-i. Find the fifth zero and then determine g(x). I understand the coefficients and kn

Algebra ->  Rational-functions -> SOLUTION: A polynomial g(x) of degree 5 whose coefficients are real numbers has zeros 2, 3, -3, and 7-i. Find the fifth zero and then determine g(x). I understand the coefficients and kn      Log On


   

Question 46791: A polynomial g(x) of degree 5 whose coefficients are real numbers has zeros 2, 3, -3, and 7-i. Find the fifth zero and then determine g(x).
I understand the coefficients and know the 5th zero would have to be 7+i. However, I'm not sure how to then determine g(x). Can anyone help me?
Thanks!
Answer by adamchapman(301) About Me  (Show Source):
You can put this solution on YOUR website!
To have all real coefficients, any complex root (7-i) must have a corresponding conjugate root, (7+i) in this case.
We Now know all the roots (values of x when g(x)=0:
2, 3, -3, 7-i and 7+i
So:
g(x)=(x-2)(x-3)(x+3)(x-7+i)(x-7-i)
I hope this helps,
Adam
P.S. please visit my website, it may be helpful to you. The address is www.geocities.com/quibowibbler