Find the nth-degree polynomial function with real coefficients satisfying the given conditions. n=4; i and 5i are zeros; f(-1)=52

Since coefficients are real this must mean that the complex roots occur in conjugate pairs. We can write: 
 

and given that f(-1)=52 we can determine a... 

 
 

so that 
 

and a=1 
this leads to 
 


 


:)