SOLUTION: write a polynomial function of least degree with integral coefficients that has the given zeros -1,2i

Algebra ->  Test  -> Lessons -> SOLUTION: write a polynomial function of least degree with integral coefficients that has the given zeros -1,2i      Log On


   

Question 527180: write a polynomial function of least degree with integral coefficients that has the given zeros -1,2i
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
If 2i is a zero of the polynomial, (x-2i) is a factor of the polynomial, and -2i must also be a zero, and (x+2i) must also be a factor.
If -1 is a zero (x+1) is a factor of the polynomial.
With those 3 factors multiplied we get
P%28x%29=%28x-2i%29%28x%2B2i%29%28x%2B1%29=%28x%5E2%2B4%29%28x%2B1%29=x%5E3%2Bx%5E2%2B4x%2B4
and that's the simplest answer.
Any integer, n can be multiplied by P(x) to yield another polynomial of grade 3, with integer coefficients and the same zeros