Question 763112


You are given three roots: 

{{{i}}} and {{{5i}}}
 since {{{i}}} is a root, so must its conjugate {{{-i}}} also be a root,  
since {{{5i}}} is a root, so must its conjugate {{{-5i}}} also be a root

You can find {{{f(x)}}} by using zero product rule 

{{{f(x)=(x+i)(x-i)(x+5i)(x-5i) }}}

{{{f(x)=(x^2-i^2)(x^2-(5i)^2)}}} 

{{{f(x)=(x^2-(-1))(x^2-25i^2)}}} 

{{{f(x)=(x^2+1)(x^2-25(-1))}}} 

{{{f(x)=(x^2+1)(x^2+25)}}} 

{{{f(x)=x^4+25x^2+x^2+25}}}

{{{f(x)=x^4+26x^2+25}}}....your polynomial


check if
 
{{{f(-1)=52}}} 

{{{f(-1)=(-1)^4+26(-1)^2+25}}}

{{{f(-1)=1+26*1+25}}}

{{{f(-1)=52}}}