SOLUTION: This is an update of a previous problem which I copied wrong I need to find a polynomial of degree 4 with integer coefficients that have roots:-2,5,and 3+2i such that P(3)=-80. I

Algebra ->  Radicals -> SOLUTION: This is an update of a previous problem which I copied wrong I need to find a polynomial of degree 4 with integer coefficients that have roots:-2,5,and 3+2i such that P(3)=-80. I      Log On


   

Question 190966: This is an update of a previous problem which I copied wrong
I need to find a polynomial of degree 4 with integer coefficients that have roots:-2,5,and 3+2i such that P(3)=-80. I know to use the conjugate of 3+2i which is 3-2i, and I know how to put them in the f(x)=a(x-r1)(x-r2...format, but from there I get tripped up and can't figure out what to do with P(3)=-80. Thanks.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


So far, so good. You have:



Now you have to multiply those 4 binomials together. Use FOIL for the two pairs of binomials and the extension of the FOIL idea to multiply the two trinomials that will result. Hint: Treat the complex numbers as a single number when you multiply the two complex factors. Once you have your polynomial function in standard form, i.e.

,

then



John