Question

Can someone help me by explaining how to get the answer for this problem please?
Write a polynomial function of minimum degree with real coefficients whose zeros include those listed.

4i and the square root of 2

Write the polynomial in standard form.

Answer 1

if one zero is \(4i\) then the other is its conjugate \(-4i\) and the polynomial is \((x-4i)(x+4i)(x-\sqrt2)\) or whatever you get when you multiply that out

Answer 2

if it said "integer" coefficients then you would need
\[(x-4i)(x+4i)(x-\sqrt2)(x+\sqrt2)\]which does seem more likely, although it is not what you wrote

Answer 3

it is not hard to multiply \((x-4i)(x+4i)\) you get
\[x^2+16\] pretty much by your eyeballs
similarly \((x-\sqrt2)(x+\sqrt2)=x^2-4\)

Answer 4

oops no it doesnt
\[(x-\sqrt2)(x+\sqrt2)=x^2-2\]

Answer 5

last job would be to multiply
\[(x^2+16)(x^2-2)\] but if it really only says "real" coefficients, then you can multiply
\[(x^2+16)(x-\sqrt2)\]