Mathcollege
posted by Mike
Find an nthdegree polynomial function with real coefficients satisfying the given conditions.
n=4;
i and 3 i are zero;
f(2)=65
f(x)=
An expression using x as the variable. Simplify your answer.

Reiny
all irrational and complex zeros come in conjugal pairs,
so if i is a zero , so is i
if 3i is a zero , so is 3i
so we have f(x) = a(xi)(x+i)(x3i)(x+3i)
f(x) = a(x^2 + 1)(x^2 + 9)
also f(2) = 65
a(4+1)((4+9) = 65
65a = 65
a = 1
f(x) = (x^2 + 1)(x^2 + 9)
or
f(x) = x^4 + 10x^2 + 9
check:
http://www.wolframalpha.com/input/?i=solve+x%5E4+%2B+10x%5E2+%2B+9%3D0
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