Question

Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. 5,i, SQUARE ROOT 11

Answer 1

I assume the given roots are 5-i and √11. (The details section has 5, i, √11.)

To ensure rational coefficients we need -√11 as a root. The complex conjugate of 5-i is 5+i so now we have all four roots.

(x+√11)(x-√11)(x-5-i)(x-5+i)=(x-√11)(x²-10x+25+1)=

(x²-11)(x²-10x+26)=x⁴-10x³+26x²-11x²+110x-286=

x⁴-10x³+15x²+110x-286 as the polynomial.