SOLUTION: n=;4; i and 3i are; zeros; f (-1)=20

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Question 1068323: n=;4;
i and 3i are; zeros;
f (-1)=20
Found 2 solutions by Boreal, Fombitz:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
the zeros are i and -i 3i and -3i, because complex roots appear in conjugate pairs.
(x^2+1) and (x^2+9) will give roots +/- i and 3i respectively.
the polynomial is a(x^4+10x^2+9)
f(-1)=20
a(1+10+9)=20
so a=1
x^4+10x^2+9 is polynomial
graph%28300%2C300%2C-10%2C10%2C-100%2C300%2Cx%5E4%2B10x%5E2%2B9%29

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming you're looking for a polynomial with real coefficients.
Complex roots come in complex conjugate pairs for polynomials with real coefficients.
f%28x%29=a%28x-i%29%28x%2Bi%29%28x-3i%29%28x%2B3i%29
f%28x%29=a%28x%5E2%2B1%29%28x%5E2%2B9%29
f%28-1%29=a%28%28-1%29%5E2%2B1%29%28%28-1%29%5E2%2B9%29=20
a%281%2B1%29%281%2B9%29=20
a%282%29%2810%29=20
20a=20
a=1
So,
f%28x%29=%28x%5E2%2B1%29%28x%5E2%2B9%29