Question

Find the function from the given zeros. 2, 3, and i

Answer 1

i tried to post but every time it is posted in other
so i write in detail.
if a,b,c+id are the zeros.
then zeros are a,b,c+id,c-id
\[f(x)=(x-a)(x-b)\left\{ x-\left( c+id \right) \right\} ~\left\{ x-\left( c-id \right) \right\}\]
\[=\left( x-a \right)\left( x-b \right)\left\{ \left( x-c \right)-\iota d \right\}\left\{ \left( x-c \right)+\iota d \right\}\]
\[=\left( x-a \right)\left( x-b \right)\left\{ \left( x-c \right)^2-\iota ^2d^2 \right\}\]
\[put~\iota^2=-1\]

Answer 2

wow that's a lot

Answer 3

need help

Answer 4

\[x = 2 \rightarrow x-2 =0\]
\[x=3 \rightarrow x-3 =0\]
\[x=i \rightarrow x^2 = i^2 = -1 \rightarrow x^2 +1 = 0\]
\[f(x) = (x-2)(x-3)(x^2+1)\]