Question

Can you please help with this one.


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.)

Answer 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

Answer 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