SOLUTION: Form a polynomial f(x) with real coefficients having the given degree and zeros Degree: 5 zeros: 4;-i;7+i F(x)=a(???)

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Question 966499: Form a polynomial f(x) with real coefficients having the given degree and zeros
Degree: 5 zeros: 4;-i;7+i
F(x)=a(???)
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!

The polynomial

f%28x%29 = %28x-4%29.%28x-i%29.%28x%2Bi%29.%28x-%287%2Bi%29%29.%28x-%287-i%29%29 = %28x-4%29.%28x%5E2%2B1%29.[%28x-7%29%5E2+%2B+1%29]

has real coefficients,  the degree  5,  the root  4,  the root  -i,  and the root 7+i.