SOLUTION: n=4 i and 2i are zeros f(-2)=120 f(x)=

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Question 1185503: n=4
i and 2i are zeros
f(-2)=120
f(x)=
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
n=4
i+and 2i are zeros

first use given zeros to find polynomial
if i+and 2i are zeros, then we also have -i+and -2i (complex zeros always come in pairs)
f%28x%29=a%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29%28x-x%5B4%5D%29+......substitute zeros
f%28x%29=a%28x-i%29%28x-%28-i%29%29%28x-2i%29%28x-%28-2i%29%29+
f%28x%29=a%28x-i%29%28x%2Bi%29%28x-2i%29%28x%2B2i%29+
f%28x%29=a%28x%5E2-i%5E2%29%28x%5E2-%282i%29%5E2%29+
f%28x%29=a%28x%5E2-%28-1%29%29%28x%5E2-4%28-1%29%29+
f%28x%29=a%28x%5E2%2B1%29%28x%5E2%2B4%29+
f%28x%29=a%28x%5E4+%2B+5x%5E2+%2B+4%29+

if f%28-2%29=120
120=a%28%28-2%29%5E4+%2B+5%28-2%29%5E2+%2B+4%29+
120=a%2840%29+
a=120%2F40+
a=3+

f%28x%29=3%28x%5E4+%2B+5x%5E2+%2B+4%29+
f%28x%29=3x%5E4+%2B+15x%5E2+%2B+12+