SOLUTION: Determine a polynomial function of lowest degree with rational coefficients that has the roots 3+2i, 3-2i , -1 (multiplicity 2). Can someone help and exlain to me how to sol

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Determine a polynomial function of lowest degree with rational coefficients that has the roots 3+2i, 3-2i , -1 (multiplicity 2). Can someone help and exlain to me how to sol      Log On


   

Question 763019: Determine a polynomial function of lowest degree with rational coefficients that has the roots 3+2i, 3-2i , -1 (multiplicity 2).
Can someone help and exlain to me how to solve this? Thank you in advance.
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
Multiplicity 2 tells us that the root -1 occurs twice, so


%28x-%28-1%29%29%28x-%28-1%29%29+

i.e.


%28x%2B1%29%5E2


Therefore the least degree would be 4:
P%28x%29+=%28x-%283%2B2i%29%29%28x-%283-2i%29%29%28x%2B1%29%5E2


:)