SOLUTION: Write a polynomial f(x) that satisfies the given conditions. Degree polynomial with integer coefficients with zeros -9i and 9/7.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Write a polynomial f(x) that satisfies the given conditions. Degree polynomial with integer coefficients with zeros -9i and 9/7.      Log On


   

Question 1168928: Write a polynomial f(x) that satisfies the given conditions.
Degree polynomial with integer coefficients with zeros -9i and 9/7.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

a polynomial f%28x%29 that satisfies the given conditions:
zeros:
+x%5B1%5D=-9i, since complex zeros always come in pairs you also have
+x%5B2%5D=9i
and
x%5B3%5D=9%2F7
three zeros=> degree 3 polynomial
use zero product theorem:
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29+++
f%28x%29=%28x-%28-9i%29%29%28x-9i%29%28x-9%2F7%29+++
f%28x%29=%28x%2B9i%29%28x-9i%29%28x-9%2F7%29+++
f%28x%29=%28x%5E2+%2B+81%29%28x-9%2F7%29+++
f%28x%29=x%5E3+-%289x%5E2%29%2F7+%2B+81x-729%2F7+++