SOLUTION: n=3; 1 and 3i are zeros

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Question 1136200: n=3; 1 and 3i are zeros
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52886) About Me  (Show Source):
You can put this solution on YOUR website!
.
The general form of a polynomial with real coefficients with the given degree and zeroes is


    f(x) = a*(x-1)*(x-3i)*(x+3i) = a%2A%28x-1%29%2A%28x%5E2%2B9%29.

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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

n=3;
1 and 3i are zeros
complex zeros always come in pairs, so you also have -3i
use zero product formula:
f%28x%29=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29...plug in given zeros
f%28x%29=%28x-1%29%28x-3i%29%28x-%28-3i%29%29
f%28x%29=%28x-1%29%28x-3i%29%28x%2B3i%29
f%28x%29=%28x-1%29%28x%5E2-%283i%29%5E2%29
f%28x%29=%28x-1%29%28x%5E2-%283%5E2%2A+i%5E2%29%29.......i%5E2=-1%29
f%28x%29=%28x-1%29%28x%5E2-%289%2A-1%29%29
f%28x%29=%28x-1%29%28x%5E2%2B9%29
f%28x%29=x%5E3-x%5E2%2B9x-9