Find the polynomial of least degree having zeros: -5i and 6+i

Assuming you are familiar with the theory... 

-5i is a root of x^2+25

6+i comes from x^2-12x+37

...their product is... 

(x^2+25)(x^2-12x+37)=
x^4-12x^3+62x^2-300x+925

(and any constant multiple of this will due)