Question 853206
Question is like this:
Find the polynomial equation with rational coefficients whose root is {{{i*sqrt(5)}}}.


Imaginary zeros of polynomial function happen in conjugate pairs.  Your example INCLUDES a zero, {{{-i*sqrt(5)}}} also.


Your function may be called g(x) and {{{g(x)=(x-i*sqrt(5))(x+i*sqrt(5))}}}
{{{g(x)=x^2-i^2*5}}} according to formula for difference of squares.
{{{g(x)=x^2-(-1)5}}}
{{{highlight(g(x)=x^2+5)}}}