Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.
4, -14, and 5 + 8i

A. f(x) = x4 - 362.5x2 + 1450x - 4984

B. f(x) = x4 - 9x3 + 32x2 - 725x + 4984

C. f(x) = x4 - 67x2 + 1450x - 4984

D. f(x) = x4 - 9x3 - 32x2 + 725x - 4984

Answer 1

start with
\[(x-4)(x+14)(x-(5+8i))(x-(5-8i))\] and then multiply out
it will be somewhat tedious, but do this first
\[(x-(5+8i))(x-(5-8i))\]

Answer 2

that one is not so hard, not nearly as hard as it seems
\[(x-(5+8i))(x-(5-8i))\]
if you are thinking "first outer inner last" then first is \(x^2\) last is \(5+8i)(5-8i)=5^2+8^2=89\) and
\[-(5+8i)x-(5-8i)x=-10x\] giving
\[x^2-10x+89\]

Answer 3

but then you still have to multiply by that first stuff
it is donkey work, if it was me i would cheat
http://www.wolframalpha.com/input/?i=%28x-4%29%28x%2B14%29%28x-%285%2B8i%29%29%28x-%285-8i%29%29
this is why computers were invented

Answer 4

LOL so then what would the final answer be..

Answer 5

C?