SOLUTION: find the nth-degree of a polynomial function n=3 3 and 4i are zeros f(1)= -102

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Question 1137185: find the nth-degree of a polynomial function
n=3
3 and 4i are zeros
f(1)= -102
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

n=3
3 and 4i are zeros->-4i is also zero (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
f%28x%29=a%28x-3%29%28x-4i%29%28x%2B4i%29
f%28x%29=a%28x-3%29%28x%5E2-%284i%29%5E2%29
f%28x%29=a%28x-3%29%28x%5E2-16i%5E2%29
f%28x%29=a%28x-3%29%28x%5E2-16%28-1%29%29
f%28x%29=a%28x-3%29%28x%5E2%2B16%29
f%28x%29=a%28x%5E3%2B16x-3x%5E2-48%29
f%28x%29=a%28x%5E3-3x%5E2%2B16x-48%29
use
f%281%29=+-102 to find a
-102=a%281%5E3-3%2A1%5E2%2B16%2A1-48%29
-102=-34a
a=-102%2F-34
a=3

f%28x%29=3%28x%5E3-3x%5E2%2B16x-48%29
f%28x%29=3x%5E3-9x%5E2%2B48x-144%29-> your solution