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Find an​ nth-degree polynomial function with real coefficients satisfying the given conditions.

n=4
2 i and 4 i are zeros;

f(-1)=85
f(x)=
​(Type an expression using x as the variable. Simplify your​ answer.)

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2 answers
  1. if it has real coefficients, then its complex roots come in conjugate pairs, meaning

    f(x) = a(x-2i)(x+2i)(x-4i)(x+4i)
    = a(x^2+4)(x^2+16)

    Now just find a that makes f(-1) = 85

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  2. for n repeated independent trials, with a constant probability of success p for all trials, find the probability of exactly x success in each of them
    a) n=5, p=1/3, x=4
    b) n=30, p=0.6, x=22

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